in the figure given above ABCD is a quadrilateral and b p d q is a parallelogram is equal to 50 cm is equal to 70 cm is equal to 60 cm and PR is equal to 40 cm if the area of the quadrilateral ABCD is 15670 square then find the area of the parallelogram bpd in cm square.
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A(APB) = 1/2 * 50*100=2500 triangle area
A(CQD) = 1/2* 70 * 100 = 3500 ...since DQ=PB=100
now ARP and BRQ are similar triangles..
so BR/PR = RQ/AR... RQ= BR/PR * AR = (60/40) * 50 = 150/2
RQ= 150/2
A(BRQ) = 1/2 * RQ * RB = 1/2 * 150/2 * 60 = 2250
A(BRC) = 1/2 * RC*RB=1/2 *(150/2+70) *60 = 4350
A(BQC) = BRC-BRQ=4350-2250=2100
BPDQ = 15600 - 2500 - 3500 - 2100 = 7500
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