Question

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

Short answer

The surface area is 184 square meters.

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

Step 2. Formula used.

$\text{Areaofrectangle}=\text{length}\times \text{width}$

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

Step 3. Calculation.

Find the area of the base of the pyramid.

$\begin{array}{c}{\text{Area}}_{\text{1}}=10\times 6\\ =60\end{array}$

The area of the two slant sides of the pyramid.

$\begin{array}{c}{\text{Area}}_{\text{2}}=2\times \left(10\times 5\right)\\ =2\times 50\\ =100\end{array}$

Find the area of the two triangular sides of pyramid.

$\begin{array}{c}{\text{Area}}_3=2\times \left(\frac{1}{2}\times 6\times 4\right)\\ =2\times 12\\ =24\end{array}$

Total surface area (A) of the figure is equal to the sum of${\text{Area}}_{\text{1}}$,${\text{Area}}_{\text{2}}$and${\text{Area}}_{\text{3}}$.

$\begin{array}{c}A=100+60+24\\ =184\end{array}$

Step 4. Conclusion.

The surface area of pyramid is 184 square meters.