PSAT Math : How to find the perimeter of a polygon

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #431 : Geometry


Note: Figure NOT drawn to scale.

Refer to the above figure. The white trapezoid is isosceles. Give the perimeter of the blue polygon.

Possible Answers:

Correct answer:


The lower base of this trapezoid is  units longer than the upper base, and being isosceles, it is symmetrical. As a result, the lower leg of the right triangle at bottom is half this difference, or 18, which is the same as the upper leg. That makes the right triangle isosceles, and, therefore, a 45-45-90 triangle. Subsequently, the hypotenuse, which is one leg of the trapezoid, has length  times a leg of the triangle, or 

The blue polygon has two sides that are the legs of this isosceles trapezoid, both of which have length ; its other three sides are of length 64, 50, 100, and 50. Add them:

Learning Tools by Varsity Tutors