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
The OA is D.
I can determine the area of each triangle and then make the sum of them to get the total area of the shaded region,
$$T_{Shaded}=\frac{1}{2}b_{APQ}\cdot h_{APQ}+\frac{1}{2}b_{CDM}\cdot h_{CDM}$$
$$T_{Shaded}=\frac{1}{2}\cdot5\cdot5+\frac{1}{2}\cdot5\cdot10=\frac{75}{2}$$
Please, can any expert explain another way to solve this PS question, please? Thanks.
