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: Find area of the square base

The base is a square with side length 16 cm (from the pyramid's base edges). Area of square = side × side = \(16 \times 16 = 256\) \(cm^2\).

Step2: Find area of one triangular face

Each triangular face has a base of 16 cm and a height of 15 cm (from the net's triangle height). Area of a triangle = \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 16 \times 15 = 120\) \(cm^2\).

Step3: Find total area of four triangular faces

There are 4 identical triangular faces. Total area of triangles = \(4 \times 120 = 480\) \(cm^2\).

Step4: Find total surface area

Surface area = area of base + total area of triangles = \(256 + 480 = 736\) \(cm^2\).

Answer:

736