Question

The surface area of a square pyramid 360 square meters. The base length is 12 meters. Determine the slant height.

Answer 1

The slant height is
`l=9 \:m`.

Explanation:

A regular pyramid is a pyramid where the base is a regular polygon.

The surface area of a regular pyramid is given by

`SA=B+(1)/(2) nbl`

where,
`B` is the area of the base,
`n` is the number of triangles,
`b` is base length, and
`l` is the slant height.

A square pyramid is a pyramid having a square base.

From the information given we know that is a square pyramid (
`n =4`), the surface area is 360
`m^2` and the base length is 12
`m`.

The area of the base is given by

`B=l^2\\\\B=12^2=144`

Applying the equation for the surface area and solving for the slant height, we get that

`SA=B+(1)/(2) nbl\\\\360=144+(1)/(2) 4\cdot 12\cdot l\\\\144+(1)/(2)\cdot \:4\cdot \:12l=360\\\\144+24l=360\\\\24l=216\\\\(24l)/(24)=(216)/(24)\\\\l=9`

The slant height is
`l=9 \:m`.

Answer 2

The slant height is 9 meters.

Explanation:

To determine the slant height, we will follow the steps below;

First, write down the formula:

Surface area = 2bs + b²

where b= the length of the base of the square pyramid

s = the slant height of the square pyramid

From the question given,

surface area of a square pyramid = 360 square meters

base length = 12 meters

We can now proceed to insert the values into the formula and then solve for s

Surface area = 2bs + b²

360 = 2(12)s + (12)²

360 = 24s + 144

subtract 144 from both-side of the equation

360 - 144 = 24s

216 = 24s

Divide both-side of the equation by 24

216/24 = 24s/24

9 = s

s = 9 meters

The slant height is 9 meters.