SOLUTION: Good day! Can you help me with this problem? Find the area of the portion of a semicircle of radius 15 meters that is outside the area of an inscribed square if the base of th

Algebra ->  Circles -> SOLUTION: Good day! Can you help me with this problem? Find the area of the portion of a semicircle of radius 15 meters that is outside the area of an inscribed square if the base of th      Log On


   

Question 1000380: Good day! Can you help me with this problem?

Find the area of the portion of a semicircle of radius 15 meters that is outside the area of an inscribed square if the base of the square lies on the diameter of the semicircle.

Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We are looking for the difference of the areas: area%5Bsemicircle%5D-area%5Bsquare%5D
We do not know the size of the square, so that is what we have to find.
Here is my sketch with lengths of segments (in meters) indicated.
I needed to use a length that is half of the side of the square.
I choose to call that length (in meters) x .
with areas in square meters.
Applying the Pythagorean theorem to the right triangle in the sketch, we get
x%5E2%2B%282x%29%5E2=15%5E2
x%5E2%2B4x%5E2=225
5x%5E2=225
x%5E2=225%2F2
x%5E2=45
So, area%5Bsquare%5D=4%2A45=180 .
Rounded to the nearest 0.01, the area (in square meters) of the portion of the semicircle that is outside the inscribed square is
area%5Bsemicircle%5D-area%5Bsquare%5D=353.43-180=highlight%28173.43%29