SOLUTION: An oval athletic field is the union of a square and semicircles at opposite ends, as shown in the figure below (http://www.webassign.net/jmodd7/8-1-034.gif). If the total area of t
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-> SOLUTION: An oval athletic field is the union of a square and semicircles at opposite ends, as shown in the figure below (http://www.webassign.net/jmodd7/8-1-034.gif). If the total area of t
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Question 1057484: An oval athletic field is the union of a square and semicircles at opposite ends, as shown in the figure below (http://www.webassign.net/jmodd7/8-1-034.gif). If the total area of the field is 1,300 square yards, find the dimensions of the square.
So I know that we have to separate the shapes, and assemble the circles. I let S equal the sides of the square, and s also represents the radius, which is half the diameter.
We are given the area, which is 1300. What I don't understand is how to incorporate this into the problem to get the answer. I was provided with a formula, but am not sure how to solve for x.
A=s^2+3.14*(s/2)^2+s^2+(1+3.14/4) Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! An oval athletic field is the union of a square and semicircles at opposite ends, as shown in the figure below (http://www.webassign.net/jmodd7/8-1-034.gif).
If the total area of the field is 1,300 square yards, find the dimensions of the square.
:
Actually s also represents the diameter of the semi-circle; r = .5s
Two semi-circles = 1 circle
:
Square area + circle area = 1300 = 1300 = 1300
Factor out s^2
divide both sides by (1+.25pi0
use your calc
s^2 = 728.129
s =
s = 26.98 ~ 27 yards, one side of the square
:
;
Check this on your calc; radius=13.5
27^2 + pi*13.5^2 = 1301.55, Because we rounded it off
