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