Question

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? note : figure not drawn to scale

Explanation:

Step1: Calculate base - area

The base of the right - rectangular pyramid is a rectangle with length $L = 16$ units and width $w=8$ units. The area of the base $B$ is given by the formula $B = L\times w$.
$B=16\times8 = 128$ square units.

Step2: Calculate the area of two triangular faces with base $L$

The formula for the area of a triangle is $A=\frac{1}{2}\times base\times height$. For the two triangular faces with base $L = 16$ units and height $h = 18$ units, the combined area $A_1$ is $2\times\frac{1}{2}\times L\times h$.
$A_1=16\times18=288$ square units.

Step3: Calculate the area of two triangular faces with base $w$

For the two triangular faces with base $w = 8$ units and height $h = 18$ units, the combined area $A_2$ is $2\times\frac{1}{2}\times w\times h$.
$A_2=8\times18 = 144$ square units.

Step4: Calculate the total surface area

The total surface area $SA$ of the pyramid is the sum of the base - area and the areas of the four triangular faces, i.e., $SA=B + A_1+A_2$.
$SA=128 + 288+144=560$ square units.

Answer:

560