Area of the grey region

Geometry Level 1

Three squares with areas 36, 4 and 16 are arrange as shown. Find the area of the grey region.


The answer is 10.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Considering my diagram, the area of the gray region is equal to the area of the triangle plus the area of the square. We have

A = 1 2 ( 2 ) ( 6 ) + 2 2 = 10 A=\dfrac{1}{2}(2)(6)+2^2=\boxed{10}

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