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

Explanation:

Step1: Calculate base - area

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

There are 4 triangular faces. So the total area of the triangular faces is $A_{triangles}=4\times A_{\triangle}=4\times120 = 480$ $cm^{2}$.

Step4: Calculate surface - area of the pyramid

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:

$736$ $cm^{2}$