Question

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

10 m
11 m
6.1 m
7 m
4 m
surface area = \boxed{} m²

Explanation:

Step1: Identify the figure's faces

This is a prism with two congruent trapezoidal bases and four rectangular lateral faces.

Step2: Calculate area of 1 trapezoidal base

The trapezoid has bases $10\ \text{m}$ and $4\ \text{m}$, height $6.1\ \text{m}$.
Area formula: $\frac{1}{2} \times (b_1 + b_2) \times h$
$\frac{1}{2} \times (10 + 4) \times 6.1 = \frac{1}{2} \times 14 \times 6.1 = 42.7\ \text{m}^2$

Step3: Calculate total area of two bases

$2 \times 42.7 = 85.4\ \text{m}^2$

Step4: Calculate area of lateral rectangles

• Rectangle 1: $11 \times 10 = 110\ \text{m}^2$
• Rectangle 2: $11 \times 7 = 77\ \text{m}^2$
• Rectangle 3: $11 \times 4 = 44\ \text{m}^2$
• Rectangle 4: $11 \times 7 = 77\ \text{m}^2$

Step5: Sum all lateral areas

$110 + 77 + 44 + 77 = 308\ \text{m}^2$

Step6: Total surface area

Add base area and lateral area:
$85.4 + 308 = 393.4$

Answer:

$393.4\ \text{m}^2$