A dinner platter is in the shape of a regular decagon. The platter has an area of 161 square inches and a side length of 4.6 inches. What is the area of each triangle? What is the height of each triangle?

Height-7

Area-16.1in^2

My teacher gave me this problem, and she checked it all, and I got it correct.

Why?

In a decagon, there are10 congruent (same size, shape, volume) triangles. So you divide the area of the whole platter (161) by 10, because there are 10 triangles, and the area divided by 10 willalways get you the same answer (i. e., like a rectangle divided into squares).

161 divided by 10 is 16.1.

To get the height, each side length is 4.6, right? If the area of each triangle is 16.1, you work backwards in the way to find the area of a triangle.

Formula - 1/2 bh

Base - 4.6

So if you multiply 16.1 times 2 (because the opposite of halving is multiplying) you get 32.2. Divide that by 4.6 and you get 7.