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