Determine the surface area of the given square pyramid, given that all of its triangular faces or congruent.
Surface area will be adding the area of all of the faces together. So what are the faces? We are given that it’s a square pyramid. So the base which is also a face is a square. And then the rest are the triangular faces. And it says that all of them are congruent. So this triangle, this triangle, this triangle, and this last triangle are all congruent. They’re all equal in measure.
This means our surface area will be equal to the area of the square plus the triangle plus the triangle plus the triangle plus the triangle. However, these are all congruent. So instead of having the triangle plus the triangle plus the triangle plus the triangle, we could just have four times the triangle.
The area of it, the area of our square will be length times width or just the side squared. Because all the sides are equal, the length and width are equal. And then, the area of a triangle is equal to one-half times the base times the height of the triangle. So let’s begin plugging in.
For the square, we have 37 inches times 37 inches plus four times the area of the triangle. So one-half times the base of 37 times the height of 44, which is equal to 1369 inches squared. That’s the area of the square plus four times 814 inches squared.
So 814 inches squared represents the area of one of the triangles. So we need to multiply by four since there are four of them and they are all equal, which is 1369 inches squared plus 3256 inches squared resulting in a surface area of 4625 square inches.