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

Question

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

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2 weeks 2021-10-06T06:18:41+00:00 2 Answers 0

The slant height is .

Step-by-step explanation:

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

The surface area of a regular pyramid is given by where, is the area of the base, is the number of triangles, is base length, and 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 ( ), the surface area is 360 and the base length is 12 .

The area of the base is given by Applying the equation for the surface area and solving for the slant height, we get that The slant height is .

The slant height is  9 meters.

Step-by-step 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.