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The figure shows parallelogram ABCD. AR , DS , BT and CV are perpendicular to line R

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by Max@Math Revolution » Fri Jul 24, 2020 12:34 am

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[GMAT math practice question]

The figure shows parallelogram ABCD. AR , DS , BT and CV are perpendicular to line RV and AR = 10cm , DS = 16cm, CV = 9cm, ST = 3cm and RS = 8cm. What is the area of parallelogram ABCD?
7.24ps.png
A. 110 cm^2
B. 122 cm^2
C. 130 cm^2
D. 144 cm^2
E. 150 cm^2
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Re: The figure shows parallelogram ABCD. AR , DS , BT and CV are perpendicular to line R

by Max@Math Revolution » Sun Jul 26, 2020 6:07 pm
=>
7.24ps(a).png
The area of the trapezoid ARSD is (1/2)(10 + 16)·8 = 104.
The area of the trapezoid CDSV is (1/2)(9 + 16)·11 = 275/2.
The area of the trapezoid BART is (1/2)(3 + 10)·11 = 143/2.
The area of the trapezoid BTVC is (1/2)(3 + 9)·8 = 48.

Then the area of ABCD is
ARSD + CDSV - BARD - BTVC
= 104 + 275/2 – 143/2 – 48
= 208/2 + 275/2 – 143/2 – 96/2
= 244/2
= 122 cm^2.

Therefore, B is the correct answer.
Answer: B
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