Question

Find the area of the red triangle.

Answer 1

Answer:

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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

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

Answer 2

Answer:

Explanation:

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

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

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