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A stage block is being covered in carpet. The

dimensions of the block are 2 feet by 3 feet by

6 feet. Every surface will need covering except

for the surface touching the floor, which is 3 feet

by 6 feet. How would you calculate the surface

area that needs covering?

54 square feet

Step-by-step explanation:

We need to find the area of the surface touching the floor and deduct it from the total surface area of the block.

The surface area of the entire block is given as:

A = 2 (lw + lh + wh)

where l = length

w = width

h = height

The dimensions of the block are 2 feet by 3 feet by 6 feet. This means that:

l = 2 feet, h = 3 feet, w = 6 feet

Therefore, the total surface area is:

A = 2[ (2 * 3) + (2 * 6) + (3 * 6) ]

A = 2 (6 + 12 + 18)

A = 2 (36)

A = 72 square feet

The area of the surface that does not need covering is:

A = 3 * 6 = 18 square feet

The surface area of the part of the block that needs covering is therefore:

A = 72 - 18 = 54 square feet