Find the area in square inches of the figure shown.

Question

Find the area in square inches of the figure shown.

8 in.

17 in.

39 in.

36 in.

A four-sided figure is formed from two right triangles that share a leg, shown by a dashed line segment. The unshared leg and hypotenuse of one triangle are longer than those of the other triangle. The figure has four labeled lengths.

1. The larger triangle has the following lengths.
2. The unshared leg is labeled 36 inches.
3. The side opposite the right angle is labeled 39 inches.
4. The smaller triangle has the following lengths.
5. The unshared leg is labeled 8 inches.
6. The side opposite the right angle is labeled 17 inches.

Answer 1

Use the Pythagorean theorem to find the common side of the top triangle. If I read your dimensions correctly, the larger triangle has one side of 36 and a hypotenuse of 39. Find the third (common) side:

X² + 36² = 39²

X = 15

Area = 1/2BH = (1/2)(15)(36) = 270 in²

We now also have the information for the bottom triangle:

Area = (1/2)*(15)(8) = 60 in²

[Just to check, 8² + 15² = 17²? Yes, it does.]

Bob