Question

1. calculate the surface area of the right regular pentagonal pyramid. the line segment labeled 1.2 m begins at the center of the pentagon and ends at one side of the pentagon.

Explanation:

Step1: Find base area

The area of a regular pentagon is $\frac{1}{2} \times \text{perimeter} \times \text{apothem}$.
Perimeter of pentagon: $5 \times 3 = 15$ m
Base area: $\frac{1}{2} \times 15 \times 1.2 = 9$ $\text{m}^2$

Step2: Find lateral face area

Each face is a triangle. Area of one triangular face: $\frac{1}{2} \times \text{base} \times \text{slant height}$
Area of 1 face: $\frac{1}{2} \times 3 \times 10 = 15$ $\text{m}^2$
Total lateral area: $5 \times 15 = 75$ $\text{m}^2$

Step3: Total surface area

Add base area and lateral area.
Total surface area: $9 + 75 = 84$ $\text{m}^2$

Answer:

$84$ $\text{m}^2$