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.

  in²

Answer 1

With apology to David W. I think this problem is easier than that (although maybe not what was expected)

The shared side is easily seen to be 15.

The area of the larger triangle is .5*36*39*15/39 and the smaller triangle is .5*8*17*15/17.

Oh, heck! It is easier to see than that...so easy, I won't even trouble to write it down.

You have 2 right triangles of which you know both legs!!!!!

In the small triangle the hypotenuse is 17 and one leg is 8, The Pythagorean theorem says the other leg is 15. In the larger triangle (and for the same reason) the smaller leg is 15 as required.

Since you now know the legs of the right triangles, the area is easy: 1/2 the product of the legs OR as I wrote previously using the other common formula for area using the sin of an angle included between 2 sides.