Q20. - 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 trapezoid with bases 10 and 4 and legs 5, h = 20.

Step-by-Step Solution

Answer

The lateral area is600 , the total area is700 and the volume is2000 .

Step 1. Given information.

Bases of isosceles trapezoid are 10 and 4 and legs 5 and height is 20.

Step 2. Write the concept.

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

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

 

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

$\text{T.A.}=\text{L.A.+2}(\frac{1}{2}(b_1+b_2)\times l)$

 

The volume of isosceles trapezoid prism is given by:

$\text{V}=(\frac{1}{2}(b_1+b_2)\times l)\times h$

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:

$\begin{array}{c}\text{L.A.}=\text{Perimeter}\times \text{Height}\\ =(10+10+5+5)\times 20\\ =\left(30\right)\times 20\\ =600{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

The total area is:

$\begin{array}{c}\text{T.A.}=\text{L.A.+2}(\frac{1}{2}(b_1+b_2)\times l)\\ =600+2(\frac{1}{2}(10+10)\times 5)\\ =600+2(10\times 5)\\ =600+100\\ =700{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

And the volume is:

$\begin{array}{c}\text{V}=(\frac{1}{2}(b_1+b_2)\times l)\times h\\ =2(\frac{1}{2}(10+10)\times 5)\times 20\\ =100\times 20\\ =2000{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$