Question

The length of the long diameter in an ellipse is 34 ft and length of the short diameter is 13 ft. Find the area of the ellipse in ft 2?

Answer 1

`A=110.5\pi\ ft^2` or
`A=346.97\ ft^2`

Explanation:

we know that

The area of an ellipse can be determined using the formula

`A=\pi xy`

where

x and y are half the lengths of the largest and smallest diameters of the ellipse

we have

`x=(34)/(2)=17\ ft`

`y=(13)/(2)=6.5\ ft`

substitute

`A=\pi (17)(6.5)`

`A=110.5\pi\ ft^2` ----> exact value of the area

Find the approximate value

assume

`\pi =3.14`

substitute

`A=110.5(3.14)=346.97\ ft^2` ----> approximate value