What is the surface area of this square pyramid? Round your answer to the nearest tenth. 122.2 yd² 192.8 yd² 244.4 yd² 513.3 yd² Note: Image not drawn to scale.

122.2 yd^2

Step-by-step explanation:

The square pyramid is made out of 4 triangles. In order to find the surface area of the pyramid we need to find the area of each triangle. We know two things, since its a square pyramid the base should be the same and this also means the triangles are all equal to each other.

First in order to find the area of the triangle we need to find the height.

I cut the facing triangle in half and i get a smaller triangle which tells me that the base is 4.2, which is half, because i know that the triangle cuts in the middle (I know this because its a square triangle so all triangles are equal.

Now i will be using tan (theta) in order to find the height.

tan ∅ =

In this case, we don't know the opposite but we know the adjacent and the angle, substituting these into the formula we get that the height is 7.3.

Now we know the height and they are for equal triangles so we can find the area of one and multiply them by 4 .

Where the base is 8.4 yards (keep in mind now we are dealing with the whole triangle not just the half.  

Then substituting b= 8.4 and h = 7.3 and then multiplying them by 4 should give us the total area.

The final formula to be used:

Substiting into the formula should give us 122.2.

Let me know if you have any questions.