Question

Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8 cm

Answer 1

The surface area of a square pyramid is: 105 cm^2

Explanation:

The surface area of a pyramid is given by the following formula

`A = l ^ 2 + 4 * (0.5) lh`

Where

l is the length of one of the sides of the square base

h is the height of the pyramid

We know that h = 8 cm and l = 5 cm

`A = 5 ^ 2 + 4 * (0.5) * 5 * 8\\\\A = 25 + 2 * (40)\\\\A = 105\ cm ^ 2`

Answer 2

105 square cm.

Explanation:

The surface area of a square pyramid is

`SA=A_(base)+4A_(lateral \ side).`

1. The base is the square with side length of 5 cm, thus

`A_(base)=5\cdot 5=25\ cm^2.`

2. The lateral side is the triangle with the base of 5 cm and the height of 8 cm. Thus,

`A_(lateral \ side)=(1)/(2)\cdot \text{base}\cdot \text{height}=(1)/(2)\cdot 5\cdot 8=20\ cm^2.`

Now, the surface area of the pyramid is

`SA=25+4\cdot 20=105\ cm^2.`