Question

type the correct answer in the box. use numerals instead of words. the composite figure shown has a surface area of 482 square inches. what is the length of the prism in inches? the length of the prism is inches.

Explanation:

Step1: Identify surface - area formula for composite prism

The composite prism has two triangular faces and three rectangular faces. The surface - area formula for a triangular prism is $SA = 2\times(\text{area of base})+\text{lateral surface area}$. The area of the triangular base with base $b = 3$ in and height $h = 4$ in is $A_{base}=\frac{1}{2}\times3\times4 = 6$ square inches. The lateral - surface area consists of three rectangles with dimensions: one with dimensions $3\times l$, one with dimensions $4\times l$, and one with dimensions $5\times l$ (where $l$ is the length of the prism), and two rectangles with dimensions $5\times l$ and $3\times l$ for the other part of the composite prism. So $SA=2\times6+(3 + 4+5)l+(5 + 3)l$.

Step2: Simplify the surface - area formula

$SA = 12+(12l + 8l)=12 + 20l$.

Step3: Solve for $l$

We know that $SA = 482$ square inches. So we set up the equation $482=12 + 20l$. Subtract 12 from both sides: $482−12=20l$, which gives $470 = 20l$. Then divide both sides by 20: $l=\frac{470}{20}=23.5$ inches.

Answer:

$23.5$