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 of the right - rectangular pyramid is a rectangle. The formula for the area of the base $B$ is $B = L\times w$, where $L = 16$ units and $w = 8$ units. So, $B=16\times8 = 128$ square units.

Step2: Calculate area of triangular faces

There are two pairs of triangular faces.
For the pair of triangular faces with base $L = 16$ and height $h$:
The area of a triangle is $A=\frac{1}{2}\times base\times height$. For the triangles with base $L = 16$ and height $h = 18$, the area of one such triangle is $A_1=\frac{1}{2}\times16\times18=144$ square units, and the area of the pair is $2A_1 = 2\times144 = 288$ square units.
For the pair of triangular faces with base $w = 8$ and height $h$:
The area of a triangle is $A=\frac{1}{2}\times base\times height$. For the triangles with base $w = 8$ and height $h = 18$, the area of one such triangle is $A_2=\frac{1}{2}\times8\times18 = 72$ square units, and the area of the pair is $2A_2=2\times72 = 144$ square units.

Step3: Calculate total surface area

The total surface area $SA$ of the right - rectangular pyramid is the sum of the base area and the areas of the four triangular faces. So, $SA=B + 2A_1+2A_2=128+288 + 144=560$ square units.

Answer:

560