SOLUTION: in square ABCD , p is the midpoint of DC and Q is the midpoint of AD. if the area of the quadrilateral QBCP is 15. what is the area of square ABCD ?

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Question 322348: in square ABCD , p is the midpoint of DC and Q is the midpoint of AD. if the area of the quadrilateral QBCP is 15. what is the area of square ABCD ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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Let the side of the square equal s.
The area of QBCP plus the area of triangle ABQ and the area of triangle PDQ equal the area of the square ABCD.
The area of the triangle is,
A=%281%2F2%29bh
ABQ:A1=%281%2F2%29%28s%2F2%29%28s%29=s%5E2%2F4
PDQ:A2=%281%2F2%29%28s%2F2%29%28s%2F2%29=s%5E2%2F8
QBCP:15
ABCD:s%5E2
Put it all together,
s%5E2%2F4%2Bs%5E2%2F8%2B15=s%5E2
2s%5E2%2Bs%5E2%2B120=8s%5E2
5s%5E2=120
s%5E2=24
s=2sqrt%286%29