Question

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

8 km
6 km
3.7 km
4 km
3 km
surface area = \boxed{} km²

Explanation:

Step1: Identify congruent faces

The figure is a prism with 2 congruent trapezoidal bases and 4 rectangular lateral faces (with opposite rectangles congruent).

Step2: Calculate area of 1 trapezoid

Area of trapezoid: $\frac{1}{2} \times (a + b) \times h$, where $a=3\ \text{km}$, $b=8\ \text{km}$, $h=3.7\ \text{km}$
$\frac{1}{2} \times (3 + 8) \times 3.7 = \frac{1}{2} \times 11 \times 3.7 = 20.35\ \text{km}^2$

Step3: Area of 2 trapezoidal bases

$2 \times 20.35 = 40.7\ \text{km}^2$

Step4: Calculate lateral rectangle areas

• Rectangle 1 (3 km × 4 km): $3 \times 4 = 12\ \text{km}^2$
• Rectangle 2 (8 km × 4 km): $8 \times 4 = 32\ \text{km}^2$
• Rectangle 3 (6 km × 4 km): $6 \times 4 = 24\ \text{km}^2$
• Rectangle 4 (congruent to rectangle 1): $12\ \text{km}^2$

Step5: Sum all lateral areas

$12 + 32 + 24 + 12 = 80\ \text{km}^2$

Step6: Total surface area

Add base and lateral areas: $40.7 + 80 = 120.7\ \text{km}^2$

Answer:

$120.7$ $\text{km}^2$