# The figure shown is a trapezoid. What is the area of the blue triangle?

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In the figure shown we have a right trapezoid that was divided into two rectangles with areas of 56 and 14, and a smaller trapezoid with area of 9. What is the area of the blue triangle?

posted Aug 25, 2018

16

The rectangles have area of 14 and 56, they have same base so heights will be 14:56=1:4
Lets say they have sides of 1 unit and 4 unit

If bases of blue and red triangles are a and b their area will be 4a/2 and 5b/2
Since the angle opposite to a & b is same, we have a/4=b/5 -->a=4b/5
Now if we subtract the area of blue triangle from the area of red triangle: 5b/2-2a=9 => 5b/2-2*4b/5=9 => b=10 => a=8
Blue triangles area is 2a=16

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