Question

The lateral surface area of the given rectangular prism is $96sqin$. What is the height of the prism?

• A. $5in$
• B. $4in$
• C. $8in$
• D. $6in$

Answer 1

The correct option is D $6in$

Let h be the height of the prism.
Lateral surface area of the given prism consists of four rectangular lateral faces $A,B,\text{and}C,D$.
Area of rectangular face $A\text{or}B=\text{Height}\times \text{Width}=h\times 3=3hsqin$
Area of rectangular face $C\text{or}D=\text{Height}\times \text{Width}=h\times 5=5hsqin$

Lateral surface area of rectangular prism $=$ Area of rectangular face $(A+B+C+D)$
$96=3h+3h+5h+5h$
$96=16h$
$h=\frac{96}{16}$
$h=6in$