Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

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

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

                                                   $SA=B+\frac{1}{2} nbl$

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

$SA=B+\frac{1}{2} nbl\\\\360=144+\frac{1}{2} 4\cdot 12\cdot l\\\\144+\frac{1}{2}\cdot \:4\cdot \:12l=360\\\\144+24l=360\\\\24l=216\\\\\frac{24l}{24}=\frac{216}{24}\\\\l=9$

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