How to find the area of the red triangle given in the pic?
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Therefore, these two triangles have a combined area equal to 1/2 the area of the parallelogram. Their area is:
Lower triangles = (c + 79 + e) + (d + 10 + f) = (area of parallelogram)/2
Now consider the triangles whose sides span the right side of the parallelogram and touch the left side of the parallelogram. As these triangles touch two opposite sides of the parallelogram, each triangle has the same horizontal distance the parallelogram does between its left and right sides.
Therefore, these triangles also have an area equal 1/2 the area of the parallelogram, and their combined areas equal:
Right triangles = (x + c + 72 + d) + (e+ 8 + f) = (area of parallelogram)/2
As both equations equal half the area of the parallelogram, we can set these areas equal to each other.
(c + 79 + e) + (d + 10 + f) = (x + c + 72 + d) + (e + 8 + f)
We can cancel the terms c, e, d, and f on both sides and then solve for x.
79 + 10 = x + 72 + 8
x = 79 + 10 – 72 – 8 = 9