Question

Find the surface area of this square pyramid. The base has area 1764 cm^2 and perimeter 168 cm.

4116 cm^2

4704 cm^2

31,038 cm^2

2940 cm^2

Answer 1

the pyramid

Answer 2

surface area, sum of all the surfaces

you're already given the area of the base, so now you need to determine the area of the sides (triangles)

now making the assumption that all sides are the same, we then only need to calculate the area for one of the triangles and multiply it by 4 in order to determine total side area

now, from the picture, you have the base and the height of the triangle, so use the area of a triangle equation
\[A= \frac{1}{2} bh\]
to determine the area of the triangle

once you have the area of one triangle, multiply it by 4 in order to determine total side area
then add the total side area to the base area to get total surface area

Answer 3

since the base is a square, then all the sides are equal. Since there are four triangle faces and 1 square base, the total surface area is going to be