Question

Jill is trying to find the area of football field with the track around it at her high school. It is composed of a rectangular middle with a semicircle on each end. The rectangular field has length 130 feet and width 50 feet. What is the area of the whole thing?

A) 6500 + 625π ft2
B) 6500 + 2500π ft2
C) 6500 + 5000π ft2
D) 7125π ft2

Answer 1

I am pretty sure it is B or C I think B

Answer 2

`(6500+625\pi) ft^(2)`

Explanation:

Refer the attached figure

Area of rectangle = Length * Breadth

So, area of rectangle ABCD : 130*50

: 6500 square feet .

Now two semicircles are on the widths of the rectangular field .

So, diameter of the semicircles on the ends of the rectangular field = 50 feet

So, radius = diameter /2 = 50/2 = 25

Formula of area of circle =
`\pi r^(2)`

Area of 2 semicircles =
`2*(\pi r^(2))/(2)`

=
`\pi 25^(2)`

=
`625\pi`

So, the total area of the field = 6500 square feet + 625π square feet

=
`(6500+625\pi) ft^(2)`

Hence the area of the whole thing
`(6500+625\pi) ft^(2)`