Question

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This prism has a right angle for a base.
What is the volume of the prism?

Explain your thinking

Answer 1

The volume of the given prism is 48 cubic units.

Explanation:

The volume of a prism can be calculated by multiplying the area of its base by its height.

The bases of the given prism are the congruent right triangles ABC and DEF.

We have been given the measures of sides AB and AC of triangle ABC.

To determine the area of ΔABC, we first need to calculate the measure of side BC using Pythagoras Theorem:

`\implies AC^2+BC^2=AB^2`

`\implies 4^2+BC^2=5^2`

`\implies 16+BC^2=25`

`\implies BC^2=9`

`\implies BC=3`

The area of a triangle is half the product of its base and height.

The base and height of a right triangle are its legs.

`\begin{aligned}\textsf{Area of base}&=\textsf{Area of $\triangle ABC$}\\\\&=(1)/(2) \cdot BC \cdot AC\\\\&=(1)/(2) \cdot 3 \cdot 4\\\\&=6\; \sf square\;units\end{aligned}`

Therefore, the area of the base of the prism is 6 square units.

Finally, to find the volume of the prism, multiply the area of the base by the height of the prism:

`\begin{aligned}\textsf{Volume of prism}&=\textsf{Area of base} \cdot \sf height\\\\&=\textsf{Area of $\triangle ABC$} \cdot \overline{CF}\\\\&=6 \cdot 8\\\\&=48\; \sf cubic\;units\end{aligned}`

Therefore, the volume of the given prism is 48 cubic units.

Answer 2

48 unit cube

Explanation:

Solution Given:

For Triangle ABC

hypotenuse AB= 5

base AC=4

By using hypotenuse law

height BC=
`√(5^2-4^2) =3`

Now Area of the right-angled triangle is 1/2 * base*height

=1/2*AC*BC=1/2*4*3=6 units square

As we know that

The volume of triangular prism: Area of base * height

over here Area of the base= Area of the Triangle and the height is the length of the prism

=6 units square*CF

=6 units square*8

=48 unit cube