Geometry – How to Find the Area of the Shaded Region

areageometry

Find the area of the shaded region in the figure below:

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I am completely stuck on how to start off this question. Please help on some guidance on how to start it off.

Best Answer

A square into 4 areas

Split the square into $8$ triangles, convince yourself you can group them into 4 pairs and each pair has same area. Let the area of the triangles be $a, b, c, d$ as illustrated above.

You are given $c + d = 20$, $b + c = 32$ and $a + d = 16$. The area of the quadrilateral (in cyan) is $$a + b = (a + d) + ( b + c) - ( c + d) = 16 + 32 -20 = 28$$

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