Perimeter of a trapezoid

The perimeter of a trapezoid where a, b, c, d are the lengths of each side  is

P = a + b + c + d

Example #1: Find the perimeter for the trapezoid below

Perimeter  = 5 + 6 + 7 + 10 = 11 + 17 = 28

Now, let us make things a little bit more interesting. How about the figure below? Can you find the perimeter for this right trapezoid?

This example is a little tricky! Although 4 sides are given, one of them cannot be used to find the perimeter of the trapezoid. Can you tell which one? Yes, you guessed it right! The side that you cannot use is AC  = 10.

The sides that you can use are AB, AD, BC, and CD. However, we have another problem. BC is missing. We need to find BC.

BC is one side of the right triangle ABC. Therefore, we can use the Pythagorean theorem to find BC. 

AC² = AB² + BC²

10² = 8² + BC²

100 = 64 + BC²

100 - 64 = BC²

36 = BC²

Since 6² = 36, BC = 6

Perimeter = AB + BC + CD + AD  = 8 + 6 + 10 + 12 = 14 + 22 = 36