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The figure shows a right triangle ABC with AB = 8, BC = 10, and three semi-circles with diam

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The figure shows a right triangle ABC with AB = 8, BC = 10, and three semi-circles with diam

by Max@Math Revolution » Fri May 01, 2020 2:49 am

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[GMAT math practice question]

The figure shows a right triangle ABC with AB = 8, BC = 10, and three semi-circles with diameters AB, AC, and BC. What is the area of the shaded region?
5.1ps.png
A. 22
B. 23
C. 24
D. 25
E. 26
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Re: The figure shows a right triangle ABC with AB = 8, BC = 10, and three semi-circles with diam

by Max@Math Revolution » Sun May 03, 2020 7:31 pm
=>

Since triangle ABC is a right triangle, we have AC = 6 with AC^2 = BC^2 - AB^2.
The area of the semi-circle with diameter AB is 4^2π/2 = 8π and the area of the semi-circle with diameter AC is 3^2π/2 = 9π/2 and the area of the semi-circle with diameter BC is 5^2π/2 = 25π/2. The area of triangle ABC is (1/2)6*8 = 24.

We can get the area of the shaded region by subtracting the area of the semi-circle with diameter BC from the sum of the area of triangle ABC and the areas of the semi-circles with diameters AB and AC.

Then the area of the shaded region is 24 + 8π +(9/2) π – (25/2) π = 24.

Therefore, C is the answer.
Answer: C
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