Question

Compare the dimensions of the prisms. How many times greater is the surface area of the green prism than the surface area of the blue prism?
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Answer 1

Answer:

The surface area of the green prism is 6.25 times greater than the surface area of the blue prism.

Step-by-step explanation:

The surface area of both prisms consists of six rectangles: top, base, front, back, left side and right side. In terms of surface area, top=base, front=back and left side=right side, so the total surface area for each prism is:

2(base area)+2(back area)+2(side area)

=2((base area)+(back area)+(side area))

Area of blue prism = 2((base area)+(back area)+(side area))

=2((4*2)+(4*10)+(2*10))

=2(8+40+20)

=2(68)

=136 cm²

Area of green prism = 2((base area)+(back area)+(side area))

=2((10*5)+(25*10)+(25*5))

=2(50+250+125)

=2(425)

=850 cm²

850cm² is 6.25 times greater than 136cm² (850/136=6.25), so therefore, the surface area of the green prism is 6.25 times greater than the surface area of the blue prism.