So to do this problem, you have to find the area of each 2d figure. To start off, you need to find the top sides. (to make this easier I won't show the work)
The pink rectangular prism has the dimensions 2 x 4 x 10 and the green has the dimensions 4 x 4 x 7. The formula for the surface area of a rectangular prism is:
2(lw + wh + lh)
We can substitute to find the surface area of both pink and green:
Pink
2(4 x 4 + 4 x 7 + 7 x 4)
2(16 + 28 + 28)
2(72)
144
Green
2(2 x 4 + 4 x 10 + 2 x 10)
2(8 + 40 + 20)
2(68)
136
The sum is 280. We have over-counted the part where the two prisms are next to each other. The area of the counted rectangle is 4 x 7 or 28. We over-counted twice, so we need to subtract 2 x 28 or 56.
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