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 $A_{base}=L\times w$.
$A_{base}=16\times8 = 128$

Step2: Calculate area of two side - triangles with base $L$

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

Step3: Calculate area of two side - triangles with base $w$

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

Step4: Calculate total surface area

The surface area $S$ of the rectangular pyramid is the sum of the base area and the areas of the four triangular faces.
$S=A_{base}+A_1+A_2$
$S=128 + 288+144$
$S=560$

Answer:

560