Q18. - Geometry

Question

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

Triangle with sides 9, 12, 15, h = 10.

Step-by-Step Solution

Answer

The lateral area is 360, the total area is468and the volume is 540.

Step 1. Given information.

Sides of triangle are 9, 12, 15 and height is 10.

Step 2. Write the concept.

The lateral area of the triangular prism is given by:

$\text{L.A.}=\text{Perimeter}\times \text{Height}$

 

The total area of the triangular prism is given by:

$\text{T.A.}=\text{L.A.+2}\left(\frac{1}{2}bh\right)$

 

The volume of triangular prism is given by:

$\text{V}=\frac{1}{2}bhl$

Step 3. Sketch the graph.

Now to draw a prism first make its base as a triangle and then sketch the length of 10 triangle from its each point, 

Thus, the prism can be obtained as:

Step 4. Determine values.

The lateral area is:

$\begin{array}{c}\text{L.A.}=\text{Perimeter}\times \text{Height}\\ =(9+12+15)\times 10\\ =36\times 10\\ =360{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

The total area is:

$\begin{array}{c}\text{T.A.}=\text{L.A.+2}\left(\frac{1}{2}bh\right)\\ =360+(12\times 9)\\ =360+108\\ =468{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

And the volume is:

$\begin{array}{c}\text{V}=\frac{1}{2}bhl\\ =\frac{1}{2}(12\times 9\times 10)\\ =\frac{1}{2}\times 1080\\ =540{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$