Question

Identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in. HELP PLEASE!!

Answer 1

`\boxed{\text{L = 90 in}^(2);\text{ S = 115 in}^(2)}`

Explanation:

Data:

s = 5 in

l = 9 in

1. Lateral surface area

The general formula for the lateral surface area L of a regular pyramid is

L =½pl

where p represents the perimeter of the base and l the slant height.

The base is a square, so

p = 4 × 5 = 20 in

L = ½pl = ½ × 20 × 9 =
`\boxed{\text{90 in}^(2)}`

2. Total surface area

Total surface area = lateral surface area + area of base

S = L + B

B = b² = 5² = 25 in²

S = 90 + 25 =
`\boxed{\text{115 in}^(2)}`