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The large square above consists of squares and isosceles...

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by AAPL » Sat Jan 06, 2018 2:11 pm
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The large square above consist of squares and isosceles right triangles. If the large square has side 4 cm, then the area of the shaded portion in square cm is?

A. 2
B. 4
C. 6
D. 8
E. 12

The OA is D.

I know that the area of the large square is 16 square cm, then the area of the shaded portion will be

16 - Small squares area, but, how can I determine the area of the squares or the area of the isosceles right triangles?

I appreciate if any expert explain this PS question for me. Thank you so much.
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by GMATGuruNY » Sat Jan 06, 2018 3:04 pm
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In the figure about, the square is divided into 32 triangles of equal size.
The unshaded area is composed of 16 of these 32 triangles.
Thus, the unshaded area constitutes 1/2 the square, implying that the shaded area also constitutes 1/2 the square.
Since the area of the square = s² = 4² = 16, the area of the shaded region = (1/2)(16) = 8.

The correct answer is D.
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