Question

HELP I DONT KNOW HOW TO DO THIS

Answer 1

Answer: 10

Explanation:

This problem depends on how you view "volume." In this case, I would view the volume as taking the surface area of the triangle, and then multiplying it by the small width it has. This will take the area and scale it across the entire volume. So, taking the area of a triangle and multiplying it by the width, you get:

`Volume=Area*Width`

`Volume=((1)/(2) bh)*w`

We weren't given the actual base, but instead given the base area. That's easily undoable since the area of a rectangle is easy. Its simply, length times width.

`Area=l*w`

We want the length here. The length of the rectangle is equivalent to the base of the triangle. Solve for the length of the rectangle to get:

`Length=Base=Area/Width`

Lets plug in this "base" value into the formula for the volume of the figure:

`Volume=((1)/(2) (A/w)h)*w`

Plug in the given values. First though, you'll notice the width cancels giving:

`Volume=((1)/(2) Ah)`

`130=((1)/(2) 26*h)`

`130=13h`

`h=10`

Answer 2

5 units

Explanation:

The base of a triangular prism is the area of the triangle, i.e. the area of the cross-section.

The "height" of this triangular prism is the depth of the shape (the wording of the question is confusing!).

Volume of the prism = area of cross-section × height

= area of triangle × depth of shape

If the volume of the prism is 130 units³ and the area of the base is 26 units², substitute these values into the above formula to find the height:

⇒ 130 = 26 × height

⇒ height = 130 ÷ 26

⇒ height = 5 units