Chapter 12.1, Problem 4PSA

a.

To determine

To find: The total surface area of a right equilateral triangular prism with dimensions as s is 6 and l is 15.

Answer to Problem 4PSA

The total area of a right triangular prism is $121.17$ .

Explanation of Solution

Given information:

A right equilateral triangular prism with dimensions as s = 6 and l =15.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle Area of equilateral triangle: $A=\frac{s^2}{4}\sqrt{3}$

s = side of equilateral triangle.

Calculation:

  

All rectangles are equal because the triangle is equilateral.

  $\begin{array}{l}A(▭)=b\times h\\ A(▭)=5\times 6\\ A(▭)=30\end{array}$

There are three rectangles.

Lateral Area:

  $\begin{array}{l}{A}_{Lateral}=3A(▭)\\ A_{Lateral}=3\times 30\\ A_{Lateral}=90\end{array}$

Area of one base:

  $\begin{array}{l}{A}_{Triangle}=\frac{s^2}{4}\sqrt{3}\\ A_{Triangle}=\frac{{\left(6\right)}^2}{4}\sqrt{3}\\ A_{Triangle}=9\sqrt{3}\\ A_{Triangle}=15.58\end{array}$

There are two triangles.

  $\begin{array}{l}{A}_{Bases}=2A_{Triangle}\\ A_{Bases}=2\times 15.58\\ A_{Bases}=31.17\end{array}$

Total Area = Lateral Area + Area of Bases

Total Area $=90+31.17$

Total Area $=121.17$

b.

To determine

To calculate: The total surface area of a right equilateral triangular prism with dimensions as s is 12 and l is10.

Answer to Problem 4PSA

The total area of a right triangular prism is $484.70$ .

Explanation of Solution

Given information:

A right equilateral triangular prism with dimensions as s = 12 and l =10.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle Area of equilateral triangle: $A=\frac{s^2}{4}\sqrt{3}$

s = side of equilateral triangle.

Calculation:

  

All rectangles are equal because the triangle is equilateral.

  $\begin{array}{l}A(▭)=b\times h\\ A(▭)=10\times 12\\ A(▭)=120\end{array}$

There are three rectangles.

Lateral Area:

  $\begin{array}{l}{A}_{Lateral}=3A(▭)\\ A_{Lateral}=3\times 120\\ A_{Lateral}=360\end{array}$

Area of one base:

  $\begin{array}{l}{A}_{Triangle}=\frac{s^2}{4}\sqrt{3}\\ A_{Triangle}=\frac{{\left(12\right)}^2}{4}\sqrt{3}\\ A_{Triangle}=36\sqrt{3}\\ A_{Triangle}=62.35\end{array}$

There are two triangles.

  $\begin{array}{l}{A}_{Bases}=2A_{Triangle}\\ A_{Bases}=2\times 62.35\\ A_{Bases}=124.70\end{array}$

Total Area = Lateral Area + Area of Bases

Total Area $=360+124.70$

Total Area $=484.70$