PERIMETER AND AREA

Contents • Introduction

• Formulae

• Solving sums

• HOT Questions

INTRODUCTION• Perimeter:

Perimeter is the distance around a 2D shape. Like in the following shape the distance of the border or the shaded portion is the Perimeter.

• Area:

Area is the inner surface of a shape or thing, it is usually a 2D shape. Like in the following shape the shaded portion is the Area of the shape.

Area

FORMULAE• In this presentation we will learn about

the following shapes:

1.Rectangle

2.Square

3.Parallelogram

4.Triangle

5.Circle

We will learn about the area and perimeter.

Perimeter is always expressed in Unit and area in Unit2.

Perimeter: 2 (Length + Breadth) means, L+B+L+B

Perimeter is 2 x (5+2) = 14 cm

Area: Length x Breadth

Area is 5 x 2

= 10 cm2

5 cm

5 cm

2 cm2 cm

5 cm

5 cm

2 cm 2 cm

Rectangle Rectangle means four side shape which has opposite sides equal.

Square• Perimeter: 4 x Side, means S+S+S+S.

Perimeter is 4 x 2

= 8 cm

• Area: Side x Side

Area is 2 x 2 = 4 cm2

2 cm

2 cm

2 cm

2 cm

2 cm

2 cm

2 cm

2 cm

Square is a shape like rectangle which has all sides equal.

Parallelogram• Perimeter: 2 (Base + Side), means

S+B+S+B.

Perimeter is

2 x (5+3) = 16 cm

• Area: Base x Altitude

Area is 5 x 3

= 15 cm2

A parallelogram is a shape which has opposite sides parallel and equal.

3 cm

5 cm

5 cm

3 cm

5 cm

5 cm

3 cm

Altitude

Triangle• Perimeter: Side + Side + Side

Perimeter is

3+4+2 = 9 cm

• Area: ½ x Base x AltitudeArea is

½ x 4 x 3 = 6 cm2

3 cm 4 cm

2 cm

4 cm

3 cm

It is a shape which has 3 sides closed.(it is half of a parallelogram.

Circle• Perimeter: 3.14 x Diameter

Perimeter is

3.14 x 4 = 12.56 cm

• Area: 3.14 x Radius x Radius

Area is 3.14 x 32

= 3.14 x 9 = 28.26 cm2

4 cm

Circle is a shape which has no edge and has a Centre point, diameter, radius(half of diameter), etc.

3 cm

SOLVING SUMS• A rectangular field is 45 m long 20 m wide, a person ran around it. How much

did he run?

Length of the field = 45 m

Breadth of the field = 20 m

Therefore, Perimeter = 2 (45+20) m = 2 x 65 m = 130 m

Ans: He covered 130 m

• A rectangular field is 10 m long and 7 m wide. What is the area of the field?

Length of the field = 10 m

Breadth of the field = 7 m

Therefore, Area = 10 x 7 m2 = 70 m2

Ans: The area is 70 m2 .

• Find the perimeter of the square which has the sides of 2 cm.

Side of the square = 25 cm

Therefore the perimeter = 25 x 4 = 100 cm

Ans: The perimeter is 100 cm.

• Find the area of the square which has the side of 7 cm.

Side of the square = 7 cm

Area of the square = 7 x 7 cm2 = 49 cm2

Ans: The area is 49 cm2

• Find the perimeter of a parallelogram which has the sides of 15 and 10 cm.

Parallel sides of the parallelogram = 15 cm

Parallel sides of the parallelogram = 10 cm

Therefore, perimeter = 2 x (10+15) = 2 x 25 = 50 cm

Ans: The perimeter is 50 cm.

• Find the area of a parallelogram which has altitude of 14 cm and base of 20 cm.

Altitude of the parallelogram = 14 cm

Base of the parallelogram = 20 cm

Therefore area = 14 x 20 = 280 cm2

Ans: Area of the parallelogram is 280 cm2

• An equilateral triangle has sides of 36 cm. A person rolled around a wire around it. What is the length of the wire?

Length of the side of the equilateral triangle = 36 cm

Therefore, perimeter = 36 x 3 = 108 cm

Ans: The length of the wire is 108 cm.

• A triangle has a base of 10 cm and has the altitude of 15 cm. Find the area of the triangle.

Base of the triangle = 10 cm

Altitude of the triangle = 15 cm

Therefore, Area = ½ x 10 x 15 = 75 cm2

Ans: The area is 75 cm2.

• Amit has a circular disc. He measured the radius which is 8 cm. What is the circumference of the circle.

Diameter of the circle = 8 x 2 = 16 cm

Therefore, perimeter is 3.14 x 16 = 50.24 cm

Ans: The circumference is 50.24 cm.

• Rajan has a wheel which has diameter of 10 cm. He wants cover it with a flat cover. For that he needs to find the area. What is the area?

Radius of the wheel = 10/2 = 5 cm

Therefore, area = 3.14 x 5 x 5 = 78.5 cm2

Ans: The area is 78.5 cm2

HOT QUESTIONS

• A man wants to fence around this shaped field. His brother wants put grass in that field. Cost of the fencing is Rs. 10 / m and cost of putting grass is Rs. 7 / m 2 . Which costs more?

Fencing: Perimeter is 2+7+7+4+10 cm

= 30 cm

Therefore, the cost is Rs. 30 x 10

= Rs 300 is cost of fencing.

Putting grass: Area of the square 7x 7

= 49 m2

Area of the rectangle 4 by 3 m

= 4 x 3 = 12 m2

Area of the triangle = ½ x 3 x 3 = 4.5 m2

Total area is 49+12+4.5 m2 = 65.5 m2

Cost is Rs. 7 x 65.5 = Rs. 458.5

Ans: Putting grass is more costly.

7 m

4 m

2 m

10 m

7 m

• A square has a same area of a triangle. The side of the square is x, and base of the triangle is also x, what will be the altitude of the triangle?

The area of the triangle = x x xTherefore, let the altitude be a

ATQ

X x a x ½ = x2

Þ a x ½ = x2 / x

Þ a = x x 2Þ a = 2xAns: the altitude is 2x

• A parallelogram has a altitude of 10 cm . And a circle has a area of equal to the area of the parallelogram. The circle also has the diameter of 10 cm. find the base of the parallelogram.

Area of the parallelogram = Area of the Circle

Therefore, Area of the circle = 3.14 x r x r

Radius = 10/2 = 5 cm

Therefore area = 3.14 x 5 x 5 = 3.14 x 25 = 78.5 cm2

Therefore base of the parallelogram = 78.5/10 = 7.85 cm

Ans: The base is 7.85 cm

THAT’S ALL

From

UJJAL SHARMA