Question

The surface area of a square pyramid if the base edge equals 1.5 and the slant height equals 4.

Answer 1

To find the surface area of a square pyramid, we need to find the area of each face and sum them up.

The base of the square pyramid is a square, so its area is calculated by squaring the length of its edge:

Area of the base = (1.5)^2 = 2.25

There are four identical triangular faces in a square pyramid. The area of each triangular face can be calculated using the formula: (0.5) * base * height, where the base is the length of the edge and the height is the slant height.

Area of each triangular face = (0.5) * 1.5 * 4 = 3

Since there are four triangular faces, their combined area is: 4 * 3 = 12

Finally, we add the area of the base and the area of the four triangular faces:

Surface area = Area of base + Combined area of the four triangular faces
Surface area = 2.25 + 12 = <<2.25+12=14.25>>14.25

Therefore, the surface area of the square pyramid, given the base edge equals 1.5 and the slant height equals 4, is 14.25 square units.