What is the surface area of this square pyramid? round your answer to the nearest tenth.

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

2. Area of triangular surfaces:

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

At = = 

Now we need to calculate the apothem Ap.

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

sinβ =  =  

Given that the triangles are equilateral, then a = L

∴ Ap = (a)(sinβ) = 8.4sin(60°) = (8.4)() = 7.275yd

So:



Therefore, the surface area of the pyramid is:

A = As + At = 70.56 + 122.22 = 192.78

10.4 is the answer for you