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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM