FIND AREA OF A ELLIPSE

The area of an ellipse with semi-axes a and b is given by

Area A = πab

Notice that when a = b, the ellipse becomes a circle with radius a, and its area is πa².

Find the area of each figure :

Problem 1 :

Solution :

a = 6 m and b = 3 m

Area of an ellipse = πab

= 22/7 × 6 × 3

Area = 56.52 m²

Problem 2 :

Solution :

a = 5 m and b = 7 m

Area of an ellipse = πab

= 22/7 × 5 × 7

Area = 110 m²

Problem 3 :

Solution :

2a = 6 m ==> a = 3 m

2b = 4 m ==> b = 2 m

Area of an ellipse = πab

= 22/7 × 3 × 2

Area = 18.84 m²

Problem 4 :

Solution :

2a = 10 cm ==> a = 5 cm

2b = 7 cm ==> b = 3.5 cm

Area of an ellipse = πab

= 22/7 × 5 × 3.5

Area = 54.95 cm²

Problem 5 :

Solution :

Given, a = 5 cm

b = 4 cm

Area of half ellipse = 1/2 × πab

= 1/2 × 22/7 × 5 × 4

Area = 31.4 cm²

Problem 6 :

Solution :

Given, a = 6.2 m

b = 4.1 m

Area of quarter ellipse = 1/4 × πab

= 1/2 × 22/7 × 6.2 × 4.1

Area = 20.0 m²

Problem 7 :

The circle and the ellipse alongside have the same area. Find the radius of the circle.

Solution :

2a = 18 m ==> a = 9 m

2b = 8 m ==> b = 4 m

Area of an ellipse = πab

= 22/7 × 9 × 4

Area = 113 m²

Area of circle = πr²

113 = 22/7 × r²

r² = (113×7)/22

r² = 35.95

r = 6 m

So, radius of circle is 6 m.