# Math Help - Area of a grass field (rectangle + 2 semicircles)

1. ## Area of a grass field (rectangle + 2 semicircles)

I'm having a hard time with this problem

A grass field is shaped like a rectangle with semicircles on both ends. The total length of the field is exactly 100 feet. How wide, to the nearest tenth of a foot, should the field be if its total area is 4,000 square feet?

Can I assume the radius of the circle is 1/2 of the width of the rectangle?

And I still am not seeing how I could solve this

2. sketch a picture?

total length of field = length of rectangle + 2 radii

width of field = 2 radii

$A = \pi r^2 + 2r(100 - 2r)$

you were given A ... solve for r.