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What is the area in square inches of the pentagon shown?

 

 Jan 12, 2020
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Going around the pentagon in reverse clockwise direction starting at the lower left-hand vertex:

Call the lower left-hand vertex (the intersection of the 12" side and the 8" side) A.

The lower right-hand vertex (the intersection of the 8" side and the 18" side) is B.

The top right-hand vertex (the intersection of the 18" side and the 6" side) is C.

The intersection of the 6" side and the 8" side is D.

The intersection of the 8" side and the 12" side is E.

 

Draw a line segmen from E parallel to the base so that it hits side BC at point X.

This creates a rectangle ABXE with sides 8" and 12"     --->     area(ABXE)  =  96 sq in.

 

Consider triangle EXC:  it is a right triangle with base 8" and height of 6"     --->     area(EXC)  =  24 sq in.

Since this is a right triangle, its hypotenuse (side CE) has length 10"  (Pythagorean Theorem).

 

The sides of triangle ECD are 10", 6", and 8", therefore, it is also a right triangle with sides 6" and 8"     --->     area(ECD)  =  24 sq in.

 

The total area can be found by adding these three non-overlapping areas.

 Jan 12, 2020

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