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

Question

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?

Answer 1

16

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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