a square pyramid and its net are shown below. what is the surface area of the pyramid? 17 cm 17 cm 15 cm 15…

Answer:

816

Explanation:

Step1: Calculate base - area

The base is a square with side length $16$ cm. The area of the base $A_{base}=s^2$, where $s = 16$ cm. So $A_{base}=16\times16=256$ $cm^2$.

Step2: Calculate area of one triangular face

The triangular face has base $b = 16$ cm and height $h = 17$ cm. The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. So $A_{\triangle}=\frac{1}{2}\times16\times17 = 136$ $cm^2$.

Step3: Calculate total area of triangular faces

There are 4 triangular faces. So $A_{triangles}=4\times A_{\triangle}=4\times136 = 560$ $cm^2$.

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. $A=A_{base}+A_{triangles}=256 + 560=816$ $cm^2$.