Question

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

Explanation:

Step1: Calculate base - area

The base is a square with side length $a = 16$ cm. The area of a square is $A_{base}=a^{2}$. So, $A_{base}=16^{2}=256$ $cm^{2}$.

Step2: Calculate area of one triangular face

The triangular faces have base $b = 16$ cm and height $h = 15$ cm. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$. So, $A_{triangle}=\frac{1}{2}\times16\times15 = 120$ $cm^{2}$.

Step3: Calculate total area of triangular faces

A square - pyramid has 4 triangular faces. The total area of the triangular faces is $A_{triangles}=4\times A_{triangle}=4\times120 = 480$ $cm^{2}$.

Step4: Calculate surface area

The surface area $A$ of the square - pyramid is the sum of the base area and the total area of the triangular faces. So, $A=A_{base}+A_{triangles}=256 + 480=736$ $cm^{2}$.

Answer:

736