Question

note : figure not drawn to scale. the figure shown is a right rectangular pyramid, where l = 16 units, w = 8 units, and h = 18 units. what is the surface area, in square units, of the pyramid?

Explanation:

Step1: Calculate base area

The base is a rectangle with length $L = 16$ and width $w=8$. The area of the base $A_{base}=L\times w = 16\times8=128$.

Step2: Calculate area of two side - faces with dimensions $L$ and $h$

The area of one face with dimensions $L = 16$ and height $h = 18$ is $A_{1}=L\times h\div2=16\times18\div2 = 144$. The area of two such faces is $2A_{1}=2\times144 = 288$.

Step3: Calculate area of two side - faces with dimensions $w$ and $h$

The area of one face with dimensions $w = 8$ and height $h = 18$ is $A_{2}=w\times h\div2=8\times18\div2=72$. The area of two such faces is $2A_{2}=2\times72 = 144$.

Step4: Calculate total surface area

The total surface area $A=A_{base}+2A_{1}+2A_{2}=128 + 288+144=560$.

Answer:

560