Area of Shaded Area

Geometry Level 2

Given that the area of rectangle $ABCD$ is $150\text{ cm}^{2}$ . E and F are midpoints of $AB$ and $BC$ respectively.Find the area of the shaded region in $\text{cm}^{2}$ .

40 30 50 60

1 solution

Yong Hao Tham
May 1, 2016

Let G be the midpoint for CD and H be the midpoint for AB

By seperating the rectangle ABCD into triangles ABD and triangles BCD, we would have two triangles with medians intersecting each other at the centroid. We know that all areas of triangles are equal when it is a result of medians and centroid.

Therefore, all 12 triangles have the same area.

Area of the shaded region=150÷12×4= $\boxed{50}$

Area of Shaded Area

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