## Calculating Perimeters

Introduction

Sum of all the edges of the regular or irregular geometric shaped objects forms the perimeter of the object and the surface occupied by the object inside the edges is called as area of the object. We have formulas to calculate the perimeter of geometric shapes like square, rectangle, parallelogram, trapezium, circle article helps us in calculating the perimeter of the given shapes.

Formulas Used for Calculating Perimeters of Various Geometrical Shapes:

Square: A square has four equal sides.

Perimeter of a square = a + a + a + a = 4a units where a is the side of the square

Rectangle: A rectangle has equal opposite sides. We call the two dimensions of the rectangle as length and width.

Perimeter of a rectangle = l + w + l + w = 2(l + w) units where l is the length of the rectangle and w is the width of the rectangle

Circle: It is a plane round figure with center. A circle is usually described with it's radius. Distance between the center of the circle and a point on the circumference of the circle is radius and two times the radius is called as diameter of the circle.

Circumference of a circle = 2?? r units where r is the radius of a circle

?? = 3.14 (constant)

Triangle: A triangle has three sides.

Perimeter of a triangle = (a + b + c) units where a, b and c are sides of the triangle.

These are the formula for calculating perimeters .

Problems on Calculating Perimeters:

Ex 1: Find out the perimeter of a square having a side of 4 cm?

Sol:

Step 1: Write the formula.

Perimeter of a square, P = 4a

Step 2: Plug the given value in the formula.

a = 4cm

P = 4 * 4

= 16cm

Step 3: Write the solution.

Ans : Perimeter of a square is 16cm

Ex 2: Calculate the perimeter of a rectangle whose length is 4 cm and width is 2 cm.

Sol:

Step 1: Write the formula.

Perimeter of a rectangle, P = 2(l + w)

Step 2: Plug the given values in the formula.

l = 4cm,

w= 2cm

P = 2(4 + 2) = 2(6) = 12cm

Step 3: Write the solution.

Ans: Perimeter of a rectangle is 12 cm

Ex 3: Calculate the perimeter of a triangle whose sides are 6 cm, 3 cm and 5 cm.

Sol:

Step 1: Write the formula.

Perimeter of a triangle, P = a + b + c

Step 2: Plug the given values in the formula.

a = 6 cm

b = 3 cm

c = 5 cm

P = 6 + 3 + 5 = 14cm

Step 3: Write the solution.

Ans: Perimeter of triangle is 14cm

Ex 4: Calculate the circumference of a circle with radius 6 cm?

Sol:

Step 1: Write the formula.

Circumference of a circle, c = 2?? r units

Step 2: Plug the given values in the formula

r = 6 cm

?? = 3.14 (constant)

C = 2 * 3.14 * 6 = 37.68 cm

Step 3: Write the solution.

Ans: Circumference of a circle is 37.68cm