Question

The bottom shape is a cube with base edges of 6 inches. The top shape is a right pyramid with a height of 4 inches. What is the surface area of this composite figure?
180 in2
60 in2
240 in2
36 in2

Answer 1

the cube has 5 surfaces exposed - this area = 5*6^2 = 180 sq ins
the pyramid has 4 trianglular surfaces each of area 15 - total 60 sq ins

total SA = 240 sq ins

Answer 2

the area of the triangles are 5* 3 because the sloping height = 5 and base = 6.
slope height is calculated by pythagoras

Answer 3

4 = height of pyramid and 3 = half base (side of cube =6)

Answer 4

The base of the composite solid is a cube comprised of 6 squares, each of side 6. Five of these square faces are exposed. One of them is covered by the base of the regular pyramid.
To this area, the lateral area of the pyramid is added. Because the pyramid's base is attached to a face of the cube, the pyramid's base is not included in the surface area total of the composite figure.
Surface Area of Composite Figure = 5*6*6 + (1/2)*perimeter of base* slant height = 180 + (1/2)*(6*4)*5 = 180 + 60 = 240 square inches.
Note: the height of the pyramid is 4 but the slant height of the pyramid is 5. It is the slant height that is needed for the surface area calculation.