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A pentagon is shown what is the area, in square inches of the pentagon

A pentagon is shown what is the area, in square inches of the pentagon-example-1
User LeslieV
by
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1 Answer

10 votes
10 votes

Answer: 37

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Step-by-step explanation:

Along the top row, label the two triangles A and B.

In the bottom row, label the figures as C, D, E. We have C and E as the two surrounding triangles and D as the rectangle.

To find the area of triangle A, we need to find the horizontal side first. Use the pythagorean theorem to get 3 inches across the horizontal portion. We have a 3-4-5 right triangle. The area of triangle A is base*height/2 = 3*4/2 = 6 square inches. Triangle B is a reflected copy of triangle A, so it has the same area.

Triangle C has an area of base*height/2 = 1*5/2 = 2.5 square inches, so does triangle E because it is a mirrored congruent copy.

The rectangle D has an area of base*height = 4*5 = 20 square inches.

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We have these areas:

  • Triangle A = 6 square inches
  • Triangle B = 6 square inches
  • Triangle C = 2.5 square inches
  • Rectangle D = 20 square inches
  • Triangle E = 2.5 square inches

To wrap things up, add up those areas

A+B+C+D+E = 6+6+2.5+20+2.5 = 37 square inches

User ToTa
by
2.9k points
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