Required: area of the polygon

Geometry Level pending

Find the area of the green polygon shown below.


The answer is 176.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The area of the green polygon is equal to the area of the rectangle enclosing it minus the areas of a trapezoid and four triangles. We have

A = 14 ( 20 ) − 1 2 [ ( 12 + 2 ) ( 4 ) + 8 ( 2 ) + 8 ( 4 ) + 10 ( 8 ) + 2 ( 12 ) ] = 176 A=14(20)-\dfrac{1}{2}[(12+2)(4)+8(2)+8(4)+10(8)+2(12)]=\boxed{176}

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