Question

Find the surface area of the prism, cylinder, or pyramid. Round to the nearest whole number.

Short answer

The surface area is 90 square centimetres.

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

Step 2. Formula used.

$\text{Areaofpyramid}=b^2$

$\text{Areaoftriangle}=\left(\frac{1}{2}\times \text{base}\times \text{height}\right)$

Step 3. Calculation.

Evaluate the area of four slant sides of pyramid.

$\begin{array}{c}{\text{Area}}_{\text{1}}=4\times \left(\frac{1}{2}\times 4\times \sqrt{85}\right)\\ =8\sqrt{85}\end{array}$

Calculate the area of the base of pyramid.

$\begin{array}{c}{\text{Area}}_{\text{2}}=4\times 4\\ =16\end{array}$

Total surface area (A) of cylinder is equal to the sum of ${\text{Area}}_{\text{1}}$and ${\text{Area}}_{\text{2}}$.

$\begin{array}{c}A=16+8\sqrt{85}\\ =90\end{array}$

Step 4. Conclusion.

The surface area of pyramid is 90 square centimetres.