If ABCD is a square with its side length is 10ft and points

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Sep 09, 2016 4:16 pm

If ABCD is a square with its side length is 10ft and points P, Q, M are midpoints of AD, AB, and BC, respectively, what is the area of region shaded as above figure?
A. 40
B. 45
C. 50
D. 75/2
E. 33
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Source: Beat The GMAT — Problem Solving | Fri Sep 09, 2016 4:16 pm

MBA Challengers: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Fri Sep 09, 2016 11:59 pm; Thanked: 20 times

by MBA Challengers » Sat Sep 10, 2016 3:40 am

Area of the smaller triangle can be solved as below:
1/2 x 5 x 5 = 25/2
Area of the bigger triangle can be solved as below:
1/2 x 5 x 10 = 25

Adding the two to get the total area of the blue shaded area, you get:
25 + 25/2 = 75/2

Thus, the answer is 75/2 which is D.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Sep 11, 2016 5:25 pm

The area of a triangle CDM is 25 and the area of a triangle APO is 25/2. The sum of areas is 25+(25/2)=75/2. Hence, the correct answer is D.

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