Question

Specifically, I need the surface are which can be found by using this formula: S= Ph+2B

Answer 1

The surface area of a prism of heigh H and base of sides a, b, and c is:

A = PH + 2B

Where P = a + b + c is the perimeter of the base and B is its area.

We can see in the figure a prism of height H = 14 in, base sides of 10 in, 10 in, and 12 in. The height of the base is also given as h = 8 in.

Calculate the perimeter of the base:

P = 10 in + 10 in + 12 in = 32 in

The area of the base is:

`B=\frac{12\text{ in }\cdot8\text{ in}}{2}=48\text{ }in^2`

Calculate the surface area:

`\begin{gathered} A=PH+2B \\ A=32\text{ in }\cdot\text{14 in}+2\cdot48\text{ }in^2 \\ A=448\text{ }in^2+96\text{ i}n^2 \\ A=544\text{ }in^2 \end{gathered}`

The area is 544 square inches