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The area of a cross section perpendicular to the base of a rectangular prism is 45 square inches. If the length and width of the base are 5 inches each,
what is the height of the prism?
The height of the prism is
inches.
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Verified Answer :

GinnyAnswer

To find the height of the rectangular prism, we start by understanding that the area of the cross section perpendicular to the base is given as 45 square inches. The cross-section area in a rectangular prism is calculated by multiplying the base area by the height of the prism.

First, let's calculate the base area of the prism. The base of the prism is a rectangle with:
- Length = 5 inches
- Width = 5 inches

The area of the base (A_base) is given by:
\(\[ A_\text{base} = \text{length} \times \text{width} \]\)
\(\[ A_\text{base} = 5 \, \text{inches} \times 5 \, \text{inches} = 25 \, \text{square inches} \]\)

Next, we know the cross-section area (A_cross-section) is 45 square inches. The cross-section area is also the product of the base area and the height of the prism (h):

\(\[ A_\text{cross-section} = A_\text{base} \times h \]\)

Substituting the given values:

\(\[ 45 \, \text{square inches} = 25 \, \text{square inches} \times h \]\)

To find the height \(\( h \)\), we solve for \(\( h \)\) by dividing both sides of the equation by the base area:

\(\[ h = \frac{45 \, \text{square inches}}{25 \, \text{square inches}} \]\)

\(\[ h = 1.8 \]\)

Therefore, the height of the prism is \(\( 1.8 \)\) inches.

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