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 $16$ cm. The area of a square is $A_{base}=s^2$, so $A_{base}=16\times16 = 256$ $cm^2$.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, the base $b = 16$ cm and the height $h = 15$ cm. So, $A_{triangle}=\frac{1}{2}\times16\times15=120$ $cm^2$.

Step3: Calculate total area of triangular faces

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

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 $A=A_{base}+A_{triangles - total}=256 + 480=736$ $cm^2$.

Answer:

736