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Crashes and Disasters | Map: Bear Fire evacuation and perimeter north…

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Crashes and disasters, crashes and disasters | map: bear fire evacuation and perimeter north of tahoe.

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The Bear Fire , burning in Tahoe National Forest, has prompted evacuation orders south of Loyalton.

The wildfire was reported around 2 p.m. on Monday, Sept. 2. As of early Tuesday, it had burned 1,391 acres (2.2 square miles), said Forest Service fire managers.

The map above shows the approximate perimeter as a black line and the mandatory evacuation area in red.

For more details of the evacuation, including warning areas, see the Genasys Protect map. The Sierra County sheriff’s office said the order covered 286 structures and 536 residents, most of them in the Sierra Brooks subdivision.

The Bear Fire is just south of the footprint of 2020’s Loyalton Fire , which burned 47,000 acres and destroyed six homes and 29 outbuildings.

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understanding area and perimeter

Understanding Area and Perimeter

Mar 29, 2012

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Understanding Area and Perimeter. Amy Boesen CS255. Perimeter. Perimeter is simply the distance around an object. Everyday applications of perimeter include the distance around a fence or the distance around a pool. To figure out the perimeter of a rectangle, simply add up all the sides.

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Understanding Area and Perimeter Amy Boesen CS255

Perimeter • Perimeter is simply the distance around an object. • Everyday applications of perimeter include the distance around a fence or the distance around a pool. • To figure out the perimeter of a rectangle, simply add up all the sides.

Calculating Perimeter • If the length of this rectangle is 10cm and it has a width of 4cm, what is the perimeter?

Calculating Perimeter cont. • There are two ways to figure this out. The first is to add all four sides. length + length + width + width = perimeter 10 + 10 + 4 + 4 = 28 • The second approach requires you to make an algebraic equation. 2(length) + 2(width) = perimeter 2(10) + 2(4) = 28

Area • Area usually deals with how much space an object covers or how much is needed to cover the object. • Everyday applications of area include how much material it will take to cover a surface.

Units • The units for perimeter and area are not the same. • For example: If we make a dog pen that is 10 feet long and 8 feet wide we would need 36 feet of fencing to surround the pen. However, if we were to calculate the area we would say that the pen covers 80 square feet.

Calculating Area • To calculate the area of a rectangle, simply multiply the length by the width. length x width = area If a rectangle has a width of 6 feet and a length of 8 feet, what is the area?

Calculating Area cont. • To calculate the area of this rectangle, you would have this equation: 6 feet x 8 feet = 48 square feet Since you are multiplying feet x feet, your answer will be square feet. Area is always answered in square units.

Perimeter of Triangles • Finding the perimeter of a triangle is very similar to finding the perimeter of a rectangle. You simply add up the three sides. • If a triangle has one side that is 22 cm long, another that is 17 cm, and a third that is 30 cm long, what is the perimeter? 22cm + 17cm + 30cm = 69cm

Area of Triangles • Finding the area of a triangle is somewhat different than finding the area of a rectangle. • With triangles we no longer can use length times width. We now use base times height. To keep it simple, we will stick to 90 degree triangles for now. • The formula for the area of triangles is: ½ x base x height

Area of Triangles cont. • The height of the triangle is the distance from the base to the point farthest away, measured along a perpendicular line. • The height of this triangle is 4 inches and the base is 6 inches, what is its area?

Area of Triangles cont. • ½ x base x height = area of triangle • ½ x 6 inches x 4 inches = 12 square inches

Distance Around a Circle • The distance around a circle is not called perimeter. It is called the circumference. • To calculate the circumference of a circle we need to use pi. The value for pi is 3.14. Pi is the ratio of the circumference to the diameter of ANY circle.

Circumference • This gives us two possible formulas to calculate the circumference of a circle. One uses radius and the other uses diameter. circumference = pi x diameter or circumference = 2 x pi x radius

Circumference cont. • If the radius of a circle is 5 cm, what is the circumference? circumference = pi x diameter c = 3.14 x 10 c = 31.4cm circumference = 2 x pi x radius c = 2 x 3.14 x 5 c = 31.4

Area of Circles • The formula for the area of circles is a bit more complicated than the others. area = pi x radius squared If a circle has a radius of 8 inches, what is its area? A = 3.14 x 8^2 A = 200.96 square inches

Summary • We have learned many formulas for finding the perimeter and area of various objects such as rectangles, squares, triangles, and circles. • We have learned that perimeter concerns how much is needed to surround an object and that area is how much is needed to cover an object.

Summary cont. • Lastly we learn that the relationship between area and perimeter is somewhat complicated. If you double the area of a square, you do not double its perimeter. However, two objects may have the same perimeters, but different areas or the same area, but different perimeters. • You will understand this relationship more after some additional practice.

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Area and Perimeter – Definition with Examples

Area and perimeter, calculating area and perimeter for different shapes, units of measurement, practice problems on area and perimeter, frequently asked questions on area and perimeter.

Perimeter for a 2-dimensional shape is the total distance around the respective shape. For the figures with straight sides such as triangle, rectangle, square or a polygon; the perimeter is the sum of lengths for all the sides.

Perimeter for a 2-dimensional Park Shape

The peripheral border in blue is the perimeter of the park.

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The area for a 2-dimensional shape is the space enclosed within the perimeter of the given shape. To calculate the area for different shapes, use different formulas based on the number of sides and other characteristics such as angles between the sides.

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The area for the park is shown in dark green color.

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The formulas for calculating the perimeter and area of a triangle ABC are:

perimeter and area of a triangle

  • Perimeter = a + b + c

                       ⇒ Perimeter = sum of the length of all sides

                       ⇒ Perimeter = a + b + c

  • Area =  1 ⁄ 2  × base × height

perimeter and area of a Square

  • Perimeter = 4a

                       ⇒ Perimeter = sum of lengths of all sides

                       ⇒ Perimeter = a + a + a + a

                       ⇒ Perimeter = 4a

                ⇒ Area = length × breadth

                ⇒ area = a × a 

                ⇒ area = a 2

perimeter and area of a Rectangle

  • Perimeter = 2 (l + b)

                       ⇒ Perimeter = l + b + l + b

                       ⇒ Perimeter = 2 × (l + b)

  • Area = l × b

Rectangle 1

       ⇒ Area = Area (ABC) + Area (ADC)

       ⇒ Area = 2 × Area (ABC)

       ⇒ Area = 2 × ( 1 ⁄ 2  × base × height)

       ⇒ Area = base × height

       ⇒ Area = l × b

If all the measurements are in centimeter, the units of measurement for the perimeter and area of different shapes are:

  • Perimeter = sum of sides

               Thus, the unit of measurement remains the same, as cm

  • Area = product of sides

               The unit of measurement is unit2 or cm2

Application

The concepts of area and perimeter are the basis for understanding Euclidean geometry and calculating the volume of solid shapes in 3-dimensional space such as cones, prism, sphere, and cylinder. Also, we use these formulas for calculating the area and perimeter for quadrilaterals and polygons comprising of sides and curves. The real-life utility of the concept is in several fields such as mapping, architecture, and surveying. The geometric representation of figures is done by sketching the distances and areas for clear understanding.

Three-dimensional objects (Shapes)

Three-dimensional objects derived from 2-dimensional shapes and land surveying in fields.

  • Different rectangles with the same perimeter can have different areas.
  • Rectangles are also known as elongated squares.

Attend this Quiz & Test your knowledge.

Incorrect Incorrect Incorrect Incorrect

How do you explain the difference between area and perimeter to a child?

Firstly, the area of a shape is the surface or flat space that the shape covers whereas the perimeter of a shape represents the distance around its boundary. Secondly, the area is measured in square units, whereas the perimeter is measured in linear units. For example, the area of a square with a length 3 cm will be (3 cm × 3 cm) = 9 square cm. Its perimeter will be 4 × 3 cm = 12 cm.

Where do we use area and perimeter in real life?

We use area and perimeter for various purposes in our day-to-day life. For example, while purchasing a house we must know its floor area and while buying wire for fencing the garden we must know its perimeter.

Is perimeter adding or multiplying the sides of a shape?

The perimeter is the measure of the boundary of a shape. To find the perimeter, you need to add the lengths of all the sides.

Given a set of shapes with the same area, which shape will have the shortest perimeter?

The circle will have the shortest perimeter.

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Area and Perimeter of Shapes | Formula and Examples

Area and Perimeter are the two fundamental properties related to 2-dimensional shapes. Defining the size and length of its boundary. By learning about the areas of 2D shapes, we can easily determine the surface areas of 3D bodies and perimeter helps us to calculate the length of the boundary of any 2D closed shape.

The method and parameters required for finding the area and perimeter are different for each shape.

In this article, we are going to learn how to find the Area and Perimeter of different shapes, with the help of solved examples.

Definition of Area

Area is a measure of a region’s size on a surface.

In simple words, area helps us to know that how much space is occupied by a closed surface in a plane. Area is defined only for closed shapes. For a 2D geometric entity, area depends upon the shape and dimensions of the entity. It is calculated in sq units of units 2 (eg: cm 2 , m 2 ).

Definition of Perimeter

Perimeter is the length of a boundary or closed path that outlines a two dimensional shape.

For curved 2D shapes such as circle and ellipse, the perimeter is called as their circumference . By calculating perimeter of a region, one can determine the length required to surround that region on its boundaries.

Table of Content

Area and Perimeter Formulas

Area and perimeter of all shapes, parallelogram, difference between area and perimeter, solved examples on area and perimeter, practice questions on area and perimeter.

The table below provides a list of area and perimeter formulas to find values of area and perimeter of various 2D shapes.

Area and Perimeter Formulas for all Shapes

Shape

Area

Perimeter

Variables description

Triangle

A = 1/2(b × h)

P = a + b + c

b = base, h = height
a,b and c are sides of triangle

Rectangle

A = l × b

P = 2(l+b)

l = length,
b = breadth

Square

A = s × s

P = 4 × s

s = side

Circle

A = πr

P = 2πr

r = radius,
π = 22/7 or 3.14

Ellipse

A = π×b

P = π(a+b)

a = semi major axis
b = semi minor axis

Parallelogram

A = b × h

P = 2(a+b)

b = base, h = height
a and b are the opposite sides

Rhombus

A = 1/2 (d1 × d2)

P = 4 × a

d1, d2 = diagonals
a = side of rhombus

Trapezium

A = 1/2 × (a+b) × h

P = Sum of all Sides

a,b = length of parallel sides,
h = height

For polygons, perimeter can be calculated as sum of lengths of its sides. And, for a regular polygon, i.e a polygon having equal sides, perimeter is calculated as n × a, where n is number of sides or edges of the polygon and a is the measure of its one side.

The 2D shapes have some specific properties related to their dimensions and orientation of their dimensions which they adhere to. They have defined formulae to calculate their area and perimeter.

Let’s discuss the formulae to calculate area and perimeter for various shapes.

A triangle is closed figure having three sides. It has three vertices. Altitude or height of a triangle is the perpendicular drawn from one of its vertex to meet the opposite side.

The side to which the perpendicular meets is called as the base of a triangle.

Area and Perimeter of Triangle

Area and Perimeter Formula of Triangle :

Area of a triangle = 1/2 × (base) × (height) Perimeter of a triangle = Sum of all three sides

A rectangle is a four sided polygon having opposite sides equal and parallel. All the angles of a rectangle are equal to 90°.

Area and Perimeter of Rectangle

Area and Perimeter Formula of Rectangle :

Area of a rectangle = length × breadth Perimeter of a rectangle = 2 × (length + breadth)

A square is a four sided polygon having all four sides equal and parallel to each other. Also, all angles of a square have a measure of 90° each. Thus, a square can be said to be a special type of rectangle having all four sides equal.

Area and Perimeter of Square

Area and Perimeter Formula of Square:

Area of a Square = (side) × (side) Perimeter of a Square = 4 × (side)

A parallelogram is a four sided polygon having opposite sides equal and parallel. The perpendicular distance between two opposite sides is called as the height of a parallelogram. The length of those sides is called as the base of a parallelogram.

Area and Perimeter of Parallelogram

Area and Perimeter Formula of Parallelogram :

Area of a Parallelogram = Base × Height Perimeter of a Parallelogram = 2 × (Sum of opposite sides)

A rhombus is a four sided polygon having all four sides equal and opposite sides being parallel to each other. The area of a rhombus is calculated by the measure of length of its diagonals.

Area and Perimeter of Rhombus

Area and Perimeter Formula of Rhombus :

Area of a Rhombus = 1/2 × ( Product of diagonals) Perimeter of a Rhombus = 4 × side

Trapezium is a four sided polygon having two opposite sides parallel to each other. The other two sides may or may not be parallel. The distance between two parallel sides is known as the height of the trapezium.

Area and Perimeter of Trapezium

Area and Perimeter Formula of Trapezium :

Area of a trapezium = 1/2 × (Sum of parallel sides) × (height) Perimeter of a trapezium = (Sum of all 4 sides)

Area and Perimeter of Circle

Area and Perimeter Formula of Circle :

Area of a Circle = πr 2 Perimeter of a Circle = 2πr

A semicircle is half of the circle whose one side is curved and other side is bounded by the diameter of the circle.

Area and Perimeter of Semicircle

Area and Perimeter Formula of semicircle :

Area of Semicircle = 1/2 × π × r2 Perimeter of Semicircle = πr + 2r

The differences between Area and Perimeter are listed in form of a table below:

Area

Perimeter

Area is a measure of a region’s size on a surface. The region is a closed 2D figure.

Perimeter is a measure of the length of boundary of any closed 2D shape.

Area is expressed in square units, such as m , cm , mm , etc.

It is expressed in units, such as m, cm, mm, etc.

Example: The space occupied by a park.

Example: The length of boundary of park.

Also, Check: Area and Perimeter Formulas Volume Formulas Diagonal Formula Surface Area Formula

Let’s solve some example problems on the Area and Perimeter formulas of different shapes.

Example 1: Find the values of perimeter and area for rectangular park having length as 40 m and the breadth as 50 m.

Given, Length of rectangle, l = 40 m Breadth of rectangle, b = 50 m We know that, Perimeter of rectangle = 2(l+b) = 2×(40+50) = 2 × 90 = 180 m. Area of rectangle = l × b = 40 × 0 = 2000 m 2 Thus, Perimeter = 180 m. and Area = 2000 m 2

Example 2: A circular running track has a radius of 7 meters. Find its circumference. Take π = 22/7.

We have, Radius, r = 7 m and Circumference of a Circle = 2πr Therefore, Circumference = 2 × (22/7) × 7 = 44 meters Thus, circumference of the circular track comes out to be 44 meters.

Example 3: The opposite sides of a parallelogram have values as 12 units and 8 units. Find the value of its perimeter.

We know that, Perimeter of parallelogram = 2 × (Sum of opposite sides) Thus, Perimeter = 2 × (12+8) = 2 × 20 = 40 units

Following are some practice questions based on calculating area and perimeter for you to solve.

Q1. Find the area of a trapezium whose parallel sides measure 12 cm and 14 cm. The distance between parallel sides is equal to 6 cm.

Q2. Calculate the perimeter of a regular pentagon having each side equal to 5 inches.

Q3. A circle has a diameter of 14 cm. Find the values of its circumference and area. Use, = 22/7.

Q4. The perimeter of a circle is 44 m. Find its radius and then calculate its area.

Area and perimeter of different shapes is essential for solving various geometric problems and real-life applications. The area helps determine the space a shape occupies , while the perimeter measures the length of boundary around it. Learning these area and perimeter formulas for shapes like triangles, rectangles, squares, circles, is crucial in fields like architecture, engineering, and design. By practicing these concepts, one can easily calculate dimensions and solve various problems, making this knowledge extremely useful for students.

Area and Perimeter – FAQs

Define area and perimeter..

Area is defined as the space occupied by a geometrical shape. Perimeter is defined as the length of boundary of a geometrical shape

What is the Difference between Area and Perimeter?

The difference between area and perimeter is that Area defines the region occupied by a 2D shape on a surface while Perimeter defines the length of the boundary on a 2D shape.

How to Find Area and Perimeter of Different Shapes?

To find area we need to multiply the dimensions of an object and To find the perimeter we need to take sum of the boundary of the object.

How to Find Area and Perimeter of Rectangle?

We can find the area of rectangle by finding the product of its length and breadth i.e. l × b and to calculate the perimeter we need to find the sum of its length and breadth and then multiply the sum by 2 i.e. Perimeter = 2(l + b)

What is Area and Perimeter of Circle Formula?

Area and Perimeter of a circle depends upon measure of its radius. Perimeter of a circle is generally called its circumference. Following are the formulae to calculate area and perimeter of a circle, Area of a Circle = π×r 2 Perimeter of a Circle = 2×π×r where, π = pi whose value is taken as 22/7 or 3.14 commonly.

What is Area and Perimeter Formula of Square?

Area of a square: A = a 2 (where a is the length of a side) Perimeter of a square: P =4 a (where a is the length of a side)

What is Area and Perimeter of Rhombus Formula?

Area of a rhombus: A =( d 1 ​× d 2 ​​)/2 (where d 1 and d 2 ​​ are the lengths of the diagonals) Perimeter of a rhombus: P =4 a (where a is the length of a side)

What is Area and Perimeter of Trapezium Formula?

Area of a trapezium: A = 1/2​( a + b ) h (where a and b are the lengths of the parallel sides and h is the height) Perimeter of a trapezium: P = a + b + c + d (where a , b , c , and d are the lengths of the four sides)

How To Calculate Perimeter for a Polygon having n Sides?

A polygon is closed 2D shape having three or more sides. When all sides of the polygon are equal in length, it is called a regular polygon. For a regular polygon, perimeter is calculated as, P = n × a where, n is the number of sides of the polygon and a is the measure of each of its sides. For a polygon, whose sides may be of different length, perimeter can be calculated as, P = Sum of all sides

How To Calculate Area of Irregular Shapes?

For a irregular shape, we try to breakdown the shape into regular shapes such as triangle, rectangle or circle, and then, calculate the areas for each of the shape individually and sum up the individual areas to get the total area of the given irregular shape.

Is there any Direct Rrelation between Area and Perimeter of 2D Shapes?

Area and Perimeter do not have any direct mathematical relationship. Both area and perimeter measure different aspects related to any 2D figure, i.e. Area is the region covered by the figure on a surface and Perimeter is the length of boundary required to outline the shape.

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KS2 - PERIMETER & AREA PPT.

KS2 - PERIMETER & AREA PPT.

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

MissAngus's Shop

Last updated

18 August 2020

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pptx, 152.35 KB

LI – I can understand and work out the area and perimeter of 2D shapes.

this is a bit of a revision lesson - discuss what we already know then go over some examples together as a class and finish with a discussion of what we’ve learned.

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    Presentation Transcript. Area and perimeter The perimeter of a shape is easy to work out. It is just the distance all the way round the edge. If the shape has straight sides, add up the lengths of all the sides. These may be given, or you may need to measure carefully along each of the sides using a ruler. 5 cm 4 cm 3 cm 6 cm 3 cm + 5 cm + 4 cm ...

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    Area and Perimeter PowerPoint.ppt - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. This document discusses area and perimeter. It provides examples of calculating the area and perimeter of different shapes by counting squares or sides. Area is measured in square units and represents the surface space of a flat object.

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    Understanding Area and Perimeter. Amy Boesen CS255. Perimeter. Perimeter is simply the distance around an object. Everyday applications of perimeter include the distance around a fence or the distance around a pool. To figure out the perimeter of a rectangle, simply add up all the sides.

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    KS2 - PERIMETER & AREA PPT. Subject: Mathematics. Age range: 7-11. Resource type: Lesson (complete) File previews. pptx, 152.35 KB. LI - I can understand and work out the area and perimeter of 2D shapes. this is a bit of a revision lesson - discuss what we already know then go over some examples together as a class and finish with a ...