Help! Geometry

• Sep 8th 2008, 11:40 AM
wynkky
Help! Geometry
The question is:

The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

Kelli
• Sep 8th 2008, 11:59 AM
Rinor Berisha
So you have a circle and a square. I think there has to be more info!
• Sep 8th 2008, 12:23 PM
Shyam
Quote:

Originally Posted by wynkky
The question is:

The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

Kelli

Let us suppose radius of the semicircular ends = r.

So, side of square = diameter of semicircle = 2r

Now area of field = Area of two semicircles + Area of square.

$1300 = 2 \times {\frac{\pi r^2}{2}} + (2r)^2$

$1300 = \pi r^2 + 4r^2$

$1300 = r^2(\pi + 4)$

$r^2 = \frac {1300}{\pi + 4}$

$r= \sqrt {182.032}$

r= 13.49 yards

Side of square = 2r = $2 \times 13.49$ = 26.98 yards.= 27 yards