Computing Areas

greatwhiteshark

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Joined
May 8, 2005
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Find area of the shaded region enclosed in a semicircle of diameter 8cm. The length of chord AB is 6cm. HINT: Triangle ABC is a right triangle.

MY WORK:

Area of triangle ABC - Area of semicircle

I first needed to find chord BC using the Pythagorean Theorem.

I found BC = 2(sqrt7)

I then used A = 1/2 times base times height to find the area of triangle ABC.

Area of triangle ABC = 6(sqrt7)

Area of semicircle = 1/2 times 3.14 times 4^2

A = 8PI

I then subtracted area of semicircle from area of triangle ABC and got 9.24 square cm. The book's answer is 9.26sq. cm. What am I doing wrong?
 
Except for the typo about what is subtracted from what, it looks good. If you use pi = 22/7 instead of 3.14 you will be closer and if you use 3.1416 you will be right on.
 
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