Question

Please help!! 10 points.

Answer 1

`\boxed{ \text{1. 59.44 in}^(2) \text{;  2. 352.7 in}^(2) \text{; 3. 471.6 in}^(2)}`

Explanation:

1. Area of base

The radius given is that of the circumcircle.

The general formula for the edge length a of a regular polygon is

a = 2Rsin(π/n)

So,

a = 2 × 5 × sin(π/5) = 10sin0.6283 = 10 × 0.5878 = 5.878 in

The general formula for the area of a regular polygon is

A = ¼na²cot(π/n)

So,

A = ¼ × 5 × 5.878²cot(π/5) = ¼ × 5 × 5.878² × 1.376 = 59.44 in²

2. Lateral area

The general formula for the lateral area L of regular prism is

L = nah

So,

L = 5 × 5.878 × 12 = 352.7 in²

3. Total area

Total surface area = lateral area + 2×base area

S = L + 2B = 352.7 + 2 × 59.44 = 471.6 in²

`\boxed{ \text{B = 59.44 in}^(2) \text{; L = 352.7 in}^(2) \text{; S = 471.6 in}^(2)}`