Here we will learn about how to find area and perimeter of a plane figures. The perimeter is used to measure the boundaries and the area is used to measure the regions enclosed.

**Perimeter: **

The length of the boundary of a closed figure is called the perimeter of the plane figure. The units of perimeter are same as that of length, i.e., m, cm, mm, etc.

**Area: **

A part of the plane enclosed by a simple closed figure is called a plane region and the measurement of plane region enclosed is called its area.

Area is measured in square units.

*The units of area and the relation between them is given below: *

*The different geometrical shapes formula of area and perimeter with examples are discussed below: *

**Perimeter and Area of Rectangle:**

● The perimeter of rectangle = 2(l + b).

● Area of rectangle = l × b; *(l and b are the length and breadth of rectangle)*

● Diagonal of rectangle = √(l² + b²)

**Perimeter and Area of the Square:**

● Perimeter of square = 4 × S.

● Area of square = S × S.

● Diagonal of square = S√2; *(S is the side of square)*

**Perimeter and Area of the Triangle: **

● Perimeter of triangle = (a + b + c);* (a, b, c are 3 sides of a triangle)*

● Area of triangle = √(s(s - a) (s - b) (s - c));* (s is the semi-perimeter of triangle)*

● S = 1/2 (a + b + c)

● Area of triangle = 1/2 × b × h;* (b base , h height)*

● Area of an equilateral triangle = (a²√3)/4; * (a is the side of triangle)*

**Perimeter and Area of the Parallelogram: **

● Perimeter of parallelogram = 2 (sum of adjacent sides)

● Area of parallelogram = base × height

**Perimeter and Area of the Rhombus: **

● Area of rhombus = base × height

● Area of rhombus = 1/2 × length of one diagonal × length of other diagonal

● Perimeter of rhombus = 4 × side

**Perimeter and Area of the Trapezium: **

● Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)

= 1/2 (p₁ + p₂) × h (p₁, p₂ are 2 parallel sides)

**Circumference and Area of Circle: **

● Circumference of circle = 2πr

= πd

**Where**, π = 3.14 or π = 22/7

r is the radius of circle

d is the diameter of circle

● Area of circle = πr²

● Area of ring = Area of outer circle - Area of inner circle.

**Word Problems on Area and Perimeter of Plane Figures:**

**1.** Dan runs around a square field of side 20 m long. Ron
runs around a rectangular field of length 30 m and breadth 10 m. Who covers
more distance? Also find the difference between the areas of square field and
rectangular field.

**Solution:**

Side of the square field = 20 m

Perimeter of the square field = 4 × length of one side

= 4 × 20 m

= 80 m

Distance covered by Dan = 80 m

Length of the rectangular field = 30 cm

Breadth of the rectangular field = 10 m

Perimeter of the rectangular field = 2 × (length + breadth)

= 2 × (30 m + 10 m)

= 2 × 40 m

= 80 m

Distance covered by Ron = 80 m

Hence both covered equal distance.

Area of the square field = side × side

= 20 m × 20 m

= 400 m\(^{2}\)

Area of the rectangular field = length × breadth

= 30 × 10 cm

= 300 m\(^{2}\)

Difference between the areas = Area of the square – area of the rectangle

= 400 m\(^{2}\) – 300 m\(^{2}\)

= 100 m\(^{2}\)

**2.** A park with sides 20 m, 30 m, 6 m, 15 m, 15 m
and 12 m is to be fenced. If the cost of fencing is $6 a metre, what is the total cost of fencing?

**Solution:**

Perimeter of the park = Sum of the length of sides

= 20 m + 30 m + 6 m + 15 m + 15 m + 12 m

= 98 m

The length of the fence = Perimeter of the park

= 98 m

Cost of fencing 1 m = $ 6

Cost of fencing 98 m = $ 6 × 98

= $ 588

**Questions and Answers on Area and Perimeter of Plane Figures:**

**1.** A rectangular playground which is 100 m and 30 m broad is
to be fenced with wire. How much wire is needed?

**Answer:** 260 m

**2.** Which is more? Area of a rectangular field of length 50 m
and breadth 20 m or area of a square field of side 40 m.

**Answer:** Square

**3.** A field is in the form of a rectangle of length 60 m and
breadth 30 m. Find the cost of fencing the field if the cost of fencing is $ 7
a metre.

**Answer:** $ 1260

**● **Mensuration

**Perimeter and Area of Rectangle**

**Area and Perimeter of the Triangle**

**Area and Perimeter of the Parallelogram**

**Circumference and Area of Circle**

**Practice Test on Area and Perimeter of Rectangle**

**Practice Test on Area and Perimeter of Square**

● Mensuration - Worksheets

**Worksheet on Area and Perimeter of Rectangles**

**Worksheet on Area and Perimeter of Squares**

**Worksheet on Circumference and Area of Circle**

**Worksheet on Area and Perimeter of Triangle**

**7th Grade Math Problems** **8th Grade Math Practice** **From Area and Perimeter to HOME PAGE**

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