Chapter 12.2, Problem 34PPS

(a)

To determine

To graph: To sketch a net for the giventriangular prism

Explanation of Solution

Given Information:

A mailer for posters is a triangular prism. The base is an equilateral triangle with sides that measures 6 inches as shown below:

  

Concept used:

Nets of 3D shapes:

A net of a 3D shape is what it looks like if it is opened out flat. A net can be folded up to make a 3D shape.

Graph:

A net for the given triangular prism can be drawn as shown below:

Interpretation:

The net of the triangular prism consists of two triangles and three rectangles. The triangles are the bases of the prism and the rectangles are the lateral faces.

For a triangular prism:

Number of faces = 5

Number of vertices = 6

Number of edges = 9

(b)

To determine

To find: The surface area of the mailer.

Answer to Problem 34PPS

The surface area of the mailer, $A=715.76$ Sq. in.

Explanation of Solution

Given Information:

A mailer for posters is a triangular prism. The base is an equilateral triangle with sides that measures 6 inches as shown below:

  

Formula used:

Surface area of triangular prism:

A triangular prism has two triangular faces and three rectangular faces. The surface area is the sum of area of two triangles and lateral surface area of all rectangles.

Calculation:

The base of given triangular prism is an equilateral triangle

∴ Total surface area of mailer = 2(area of equilateral triangle) +3 (area of rectangle) Area of equilateral triangle:

Length of each side, $a=6$ in.

Area = $\frac{\sqrt{3}}{4}{a}^2$

  $=\frac{\sqrt{3}}{4}{6}^2$

  $=15.588$ Sq. in.

Area of rectangle: $$

Length, $l=6$ in.

Width, $b=38$ in.

Area $=lb$

  $=6\times 38$

  $=228$ Sq. in.

Total surface area of mailer = 2(area of equilateral triangle) + 3 (area of rectangle) $\begin{array}{c}A=2\left(15.88\right)+3\left(228\right)\\ =31.76+684\end{array}$

∴$A=715.76$ Sq. in.