## Tuesday, April 22, 2014

Category: Plane Geometry

"Published in Newark, California, USA"

Find the area of the rectilinear figure shown, if it is the difference between two isosceles trapezoids whose corresponding sides area parallel.

 Photo by Math Principles in Everyday Life

Solution:

The given plane figure consists of the difference of two isosceles trapezoids. Let's analyze and label further the above figure as follows

 Photo by Math Principles in Everyday Life

The area of a large trapezoid is

Before we solve for the area of a small trapezoid, we need to solve for the variables first.

Using Pythagorean Theorem

The height of a small trapezoid is

Since the given two trapezoids are isosceles trapezoid with the common thickness which is 2", then we can solve for the variables by using similar triangles.

Using similar triangles

The length of the upper base of a small trapezoid is

Using similar triangles

The length of the lower base of a small trapezoid is

Hence, the area of a small trapezoid is

Therefore, the area of a plane figure is