Question

1. sara purchased a porcelain sculpture that is in the shape of a square pyramid. the slant height is 6.1 inches and the base 6.4 inches. find the surface area. round to the nearest tenth.

Explanation:

Step1: Find base area

The base is a square with side length $s = 6.4$ inches. The formula for the area of a square is $A_{base}=s^{2}$. So, $A_{base}=6.4^{2}=40.96$ square - inches.

Step2: Find area of one triangular face

The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}bh$, where the base $b$ of the triangular face is the side - length of the base of the pyramid ($b = 6.4$ inches) and the height $h$ is the slant height ($h = 6.1$ inches). So, $A_{triangle}=\frac{1}{2}\times6.4\times6.1 = 19.52$ square - inches.

Step3: Find area of four triangular faces

Since there are 4 triangular faces in a square pyramid, $A_{triangles}=4\times A_{triangle}=4\times19.52 = 78.08$ square - inches.

Step4: Find total surface area

The total surface area $A$ of a square pyramid is the sum of the base area and the area of the four triangular faces. So, $A=A_{base}+A_{triangles}=40.96 + 78.08=119.04\approx119.0$ square - inches.

Answer:

$119.0$ square inches