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# geometry question

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

Jun 27, 2018

#1
+7616
+2

Let's divide the pentagon into shapes like this:

By SSS congruency, the two triangles at the top are congruent, and so they have the same area.

area of one of the triangles  =  (1/2)(base)(height)  =  (1/2)(8)(6)  =  24  sq inches

area of rectangle  =  (length)(width)  =  (12)(8)  =  96  sq inches

area of pentagon  =  area of rectangle + 2(area of one of the triangles)

area of pentagon  =  96 sq inches + 2(24 sq inches)

area of pentagon  =  96 sq inches + 48 sq inches

area of pentagon  =  144 sq inches

Jun 27, 2018

#1
+7616
+2

Let's divide the pentagon into shapes like this:

By SSS congruency, the two triangles at the top are congruent, and so they have the same area.

area of one of the triangles  =  (1/2)(base)(height)  =  (1/2)(8)(6)  =  24  sq inches

area of rectangle  =  (length)(width)  =  (12)(8)  =  96  sq inches

area of pentagon  =  area of rectangle + 2(area of one of the triangles)

area of pentagon  =  96 sq inches + 2(24 sq inches)

area of pentagon  =  96 sq inches + 48 sq inches

area of pentagon  =  144 sq inches

hectictar Jun 27, 2018
#2
+100588
+1

Very nice, hectictar.....!!!....this one had me stumped  !!!!

CPhill  Jun 27, 2018