Question

Dana is given the total surface area of a rectangular pyramid. She is asked for the lateral surface area. Describe how Dana can use the given information to determine the lateral surface area.

Answer 1

To get the lateral surface area, dana will subtract the two base area from the total surface area.

Total surface area of rectangular prism

The total surface area of a rectangular prism is the sum of the areas of all of the faces or surfaces that enclose the solid. Therefore,

• 2lw + 2wh + 2lh

where

l = length

w = width

h = height

Lateral surface area of a rectangular prism

The lateral surface area of a rectangular prism is the surface area of the solid without the bases.

Therefore,

• LA =  2 ( l + w ) h

Total surface area = Lateral surface area + 2 (Base Area)

Total surface area =  2 (l + w) h + 2 (l x w) = 2lh + 2wh + 2lw

Therefore,

Lateral surface area = Total surface area - 2 (Base Area)

To get the lateral surface area, dana will subtract the two base area from the total surface area.

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