Question

1. find the surface area of the following figure. round to the nearest tenth as needed.

10 mi
7 mi
3.7 mi
4 mi
4 mi
surface area = \boxed{} mi2

Explanation:

Step1: Identify shape & formula

This is a prism with 2 congruent trapezoidal bases and 4 rectangular lateral faces.
Surface Area = $2\times\text{Area of trapezoid} + \text{Sum of lateral rectangles}$

Step2: Calculate trapezoid area

Trapezoid: bases $10\ \text{mi}, 4\ \text{mi}$, height $3.7\ \text{mi}$
$\text{Area of trapezoid} = \frac{1}{2}\times(10+4)\times3.7 = \frac{1}{2}\times14\times3.7 = 25.9\ \text{mi}^2$

Step3: Calculate total base area

$2\times25.9 = 51.8\ \text{mi}^2$

Step4: Calculate lateral rectangle areas

• Rectangle 1: $10\times7 = 70\ \text{mi}^2$
• Rectangle 2: $4\times7 = 28\ \text{mi}^2$
• Rectangle 3: $4\times7 = 28\ \text{mi}^2$
• Rectangle 4: $4\times7 = 28\ \text{mi}^2$

Sum: $70+28+28+28 = 154\ \text{mi}^2$

Step5: Total surface area

Add base and lateral areas: $51.8 + 154 = 205.8$

Answer:

$205.8$ $\text{mi}^2$