Question

What is the surface area of this square pyramid?

Round your answer to the nearest tenth.

Answer 1

The answer is 192.8 yd²

Answer 2

The question is to find the surface area of the square pyramid:

This pyramid encloses a volume V, so it has five surfaces, namely:

*One square base.
*four triangular surfaces.

1. Surface area of the square base:

All four sides are equal, so:

As = LxL = (8.4yd)(8.4yd) = 70.56
`yd^2`

2. Area of triangular surfaces:

Given that the angle β=60°, we have four equilateral triangles which have three equal sides each, therefore:

At =
`4((base.height)/(2))` =
`2L.Ap`

Now we need to calculate the apothem Ap.

Using trigonometry, we can calculate Ap using the sine function:

sinβ =
`(opposite)/(hypotenuse)` =
`(Ap)/(a)`

Given that the triangles are equilateral, then a = L

∴ Ap = (a)(sinβ) = 8.4sin(60°) = (8.4)(
`( √(3) )/(2)`) = 7.275yd

So:


`At = 2(8.4)(7.275) = 122.22 yd^(2)`

Therefore, the surface area of the pyramid is:

A = As + At = 70.56 + 122.22 = 192.78
`yd^(2)`