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 $L = 16$ units and width $w=8$ units. The area of the base $A_{base}=L\times w$.
$A_{base}=16\times8 = 128$ square units.

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

The two side - faces have dimensions length $L = 16$ units and height $h = 18$ units. The area of one such face is $A_{1}=L\times h$, and the area of two such faces is $A_{2}=2\times L\times h$.
$A_{2}=2\times16\times18=576$ square units.

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

The two side - faces have dimensions width $w = 8$ units and height $h = 18$ units. The area of one such face is $A_{3}=w\times h$, and the area of two such faces is $A_{4}=2\times w\times h$.
$A_{4}=2\times8\times18 = 288$ square units.

Step4: Calculate the total surface area

The total surface area $A$ of the rectangular pyramid is the sum of the base - area and the areas of the four side - faces.
$A=A_{base}+A_{2}+A_{4}=128 + 576+288=992$ square units.

Answer:

992