Question

Find the surface area of the square pyramid.

Answer 1

`39 yd^2`

Explanation:

So, let's start by calculating the surface area of the base, which in this case is a square. The area of a square can be calculating by taking any of the lengths and squaring it, since all the sides should be equal if it's a square. Since one of the sides of the square is 3 yd, you have the equation:
`(3 yd)^2 = 9yd^2`. Now to calculate the area of the four triangles. The area of a triangle can be calculating by using the formula:
`(1)/(2)bh`, and in this case the base is 3 yd, and the height is 5 yd (lengths can be determined by looking at the given values in the diagram). But there's 4 of the triangles so we multiply it all by 4, and this gives you the equation:
`4((1)/(2)(5 yd)(3 yd)) = 4((15 yd^2)/(2)) = 4(7.5 yd^2)=30yd^2`. So now all that's left is to add this to the area of the square which gives you the equation:
`30yd^2+9yd^2=39yd^2` which is the surface area