Question

a square pyramid and its net are shown below. what is the surface area of the pyramid? 17 cm 17 cm 15 cm 15 cm 16 cm 16 cm type the answer in the box. square centimeters

Explanation:

Step1: Calculate the area of the square base

The side length of the square base is \(16\) cm. The area of a square is \(A = s^2\), so \(A_{base}=16\times16 = 256\) \(cm^2\).

Step2: Calculate the area of one triangular face

The base of each triangular face is \(16\) cm and the height is \(15\) cm. The area of a triangle is \(A=\frac{1}{2}bh\), so \(A_{triangle}=\frac{1}{2}\times16\times15= 120\) \(cm^2\).

Step3: Calculate the total area of the four triangular faces

Since there are \(4\) triangular faces, \(A_{triangles}=4\times120 = 480\) \(cm^2\).

Step4: Calculate the total surface area of the pyramid

The total surface area \(A = A_{base}+A_{triangles}\), so \(A=256 + 480=736\) \(cm^2\).

Answer:

\(736\)