Question

Help with number three make sure you answer a and B

Answer 1

Question A:

- The volume of every prism, whether it is a triangular prism-like the question gives or any other type of prism- is given as

`V=\text{ Base Area}*\text{ Height}`

- This means that Shino is correct to say that the volume of the prism is

`\begin{gathered} V=Bh \\ where, \\ B=\text{ Area of the Base} \end{gathered}`

- Thus, Shino is correct.

- However, since the base of the prism is a right triangle with a height of l and a base of w, it means we can further develop Shino's formula by substituting the formula for the area of the triangular base.

- The area of a triangle is

`\begin{gathered} B=(1)/(2)* base* height \\ \\ \text{ We have been given} \\ base=w,height=l \\ \\ \therefore B=(1)/(2)* w* l=(wl)/(2) \end{gathered}`

- Thus, if that gives the formula for the base of the triangular prism, then, we can update the formula for the volume of the as follows:

`\begin{gathered} V=B* h \\ B=(wl)/(2) \\ \\ \therefore V=(wl)/(2)* h \\ \\ V=(1)/(2)lwh \end{gathered}`

- This is the exact formula that Angelo gets. This means that Angelo is also right

Question B:

- We are given

`\begin{gathered} w=2 \\ l=4 \\ h=1.5 \end{gathered}`

- Thus, we can find the volume of the prism as follows:

`\begin{gathered} V=(1)/(2)* w* l* h \\ \\ V=(1)/(2)*2*4*1.5 \\ \\ V=6cm^3 \end{gathered}`

- Thus, the volume of the prism is 6cm³