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

Explanation:

Step1: Find area of the square base

The base is a square with side length 16 cm. The area of a square is $side^2$, so the area of the base is $16 \times 16 = 256$ $cm^2$.

Step2: Find area of one triangular face

Each triangular face has a base of 16 cm and a height of 15 cm. The area of a triangle is $\frac{1}{2} \times base \times height$, so the area of one triangle is $\frac{1}{2} \times 16 \times 15 = 120$ $cm^2$.

Step3: Find total area of four triangular faces

There are four triangular faces, so the total area of the triangles is $4 \times 120 = 480$ $cm^2$.

Step4: Find total surface area

The surface area of the square pyramid is the sum of the area of the base and the total area of the four triangular faces. So, $256 + 480 = 736$ $cm^2$.

Answer:

The surface area of the square pyramid is $\boxed{736}$ square centimeters.