Question

The surface area of a square pyramid is 85 square meters. The base length is 5 meters. What is the slant height?

Answer 1

check the picture below.

so... notice, the base, is a square, thus is called a square pyramid, is a 5x5 square, that gives us an area of 25.

but we know the total surface area is 85 though, so, if we subtract or take away the base's area of 25, 85 - 25 = 60, what's leftover is just the area of the 4 triangular faces.

now, the triangles are all equal, so they go evenly in the area of 60, therefore 60/4 is the area of one of the triangular faces, namely 15.

so, now we know the area of one of the triangles is 15, and we know its base is 5, what's the altitude of it? which incidentally is the slant-height of the pyramid.


`\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh\quad \begin{cases} A=15\\ b=5 \end{cases}\implies 15=\cfrac{5h}{2}\implies \cfrac{30}{5}=h\implies 6=h`