GRE Math Challenge #29 : What is the area of the shaded figure inside the rectangle?

GRE Math Challenge Question #29 : 

What is the area of the shaded figure inside the rectangle?

A. 18
B. 54
C. 60
D. 72
E. 91

Explanation:

The triangles inside the rectangle must be right triangles. To get the width of the rectangle, use the Pythagorean theorem: 3² + x² = 18. x = 3, and the width is twice that, or 6. 

This means the area of the shaded figure is the area of the rectangle minus the area of all 4 triangles. This is 12 × 6 − 4 × ( 1/2 × 3 × 3). This equals 54

Correct Choice : B (54)


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