In the figure given above, ABCD is a quadrilateral and BPDQ is parallelogram. AR = 50 cm, CQ = 70 cm, BR = 60, and PR = 40 cm. If the area of the quadrilateral ABCD is `15,600cm^(2)`, then find the area of then find the area of the parallelogram BPDQ (in `cm^(2)`).

Options

A. 9460
B. 8460
C. 7500
D. 9000

Answer

C

Explanation

BPDQ is a parallelogram.
`BP=DQ=BR+PR=60+40=100cm`
Area of a quadrilateral
`=(1)/(2)h(d_(1)+d_(2))=(1)/(2)AC(BR+DQ)` ltBrgt `(1)/(2)xxAC(60+100)=16,000`
`ACxx(160)/(2)=15,600`
AC = 195 cm
`AC=AR+RQ+CQ=50+RA+70=195`
`thereforeRQ=195-120`
RQ = 75 cm
RQ is the perpendicular distance between `bar(BP)` and `bar(DQ)`.
`therefore"Area of the parallelogram BPDQ"="base"xx"height"` ltBrgt `=BPxxRQ=100xx75=7500cm^(2)`