surface are composite figures

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The surface area is the surface area of the cube (less one side) 5 x 15 x 15 = 1125

To find the surface area of the triangles of the pyramid we need to find the slant height of the triangles.  To do this, we use the Pythg. Thm. 7.5^2 + 9^2 = (slant-height)^2;  This gives us a slant height of 11.715.

The area of the four triangles would be 4 x 0.5 x 15 x 11.715 = 351.45

Adding the two, we get a surface area of 1125 + 351.45 = 1476.45 square feet

For volume, we add the volume of the cube to the volume of the pyramid:

Cube: 15 x 15 x 15 = 3375

Pyramid: 1/3 x 15 x 15 x 9 = 675

Total volume = 4050 cubic feet

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ofengyvss63 (543)
New York University

Very useful material for studying!