Q19. - 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.

Isosceles triangle with sides 13, 13, 10, h = 7.

Step-by-Step Solution

Answer

The lateral area is 252, the total area is382 and the volume is455 .

Step 1. Given information.

Sides of isosceles triangle are 13, 13, 10 and height is 7.

Step 2. Write the concept.

The lateral area of the isosceles triangular prism is given by:

$\text{L.A.}=(2\times \text{Length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}equal\hspace{0.17em}\hspace{0.17em}sides}+\text{Another\hspace{0.17em}\hspace{0.17em}side})\times \text{Height}$

 The total area of the isosceles triangular prism is given by:

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

 The volume of isosceles 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:

$\begin{array}{c}\text{L.A.}=(2\times \text{Length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}equal\hspace{0.17em}\hspace{0.17em}sides}+\text{Another\hspace{0.17em}\hspace{0.17em}side})\times \text{Height}\\ =(2\times 13+10)\times 7\\ =36\times 7\\ =252{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

The total area is:

$\begin{array}{c}\text{T.A.}=\text{L.A.+2}\left(\frac{1}{2}bh\right)\\ =252+(13\times 10)\\ =252+130\\ =382{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

And the volume is:

$\begin{array}{c}\text{V}=\frac{1}{2}bhl\\ =\frac{1}{2}(13\times 10\times 7)\\ =\frac{1}{2}\times 910\\ =455{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$