Chapter 12.4, Problem 9PSB

Solution

To Calculate: The volume and the total area of prism.

The volume and the total area of prism are $300$ cm ${}^3$ and $30$ cm ${}^2$

Given information:

The measures of the sides of the prism are as follows:

AB = $10$

AE = $13$

ED = $24$

Formula used:

Here, we are using the formula:

Area of a triangle = $\frac{1}{2}\times$ base $\times$ height

(Where,base is EFand height isAF)

And, volume = Area $\times$ height

(where height is AB)

Calculation:

  

Here, In $\Delta AEF$

  ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(perpendicular\right)}^2$

  ${\left(AE\right)}^2={\left(EF\right)}^2+{\left(AF\right)}^2$

  ${\left(13\right)}^2={\left(12\right)}^2+{\left(AF\right)}^2$

  $AF=\sqrt{169-144}$

  $AF=\sqrt{25}$

  $AF=5$

So, area of cross section = $\frac{1}{2}\times$ base $\times$ height

(Here, EF is base and AF is height)

➜ $\frac{1}{2}\times 12\times 5$

➜ $30$ cm ${}^2$

And, volume of the prism = Area $\times$ height

(where height is AB)

➜ $30\times 10=300$ cm ${}^3$

Conclusion: Hence, the volume and the total area of prism are $300$ cm ${}^3$ and $30$ cm ${}^2$