The volume of a triangular prism can be found by multiplying the base times the height.

Both of the pictures of the Triangular prisms below illustrate the same formula. The formula, in general, is the area of the base (the red triangle in the picture on the left) times the height,h. The right hand picture illustrates the same formula.

Please look at pictures above

Definitions

BASE - The bottom of something considered in its support

HEIGHT - The measure from **base** to **top**

VOLUME - An amount or quantity of something, especially when great.

FORMULA - 1. a mathematical relationship or rule expressed in symbols.

If the volume equals the quantity of something when great then the volume of a triangular prism I have to say is triangular base x height.

Let's look at the base

and I picture your question like in above pictures with the top right ( please look at above 4 pictures ) being example.

THE BASE OF PICTURE ABOVE

The top right picture where **c** is in **red** and the shape is a triangle.

Let us assume we want to poor water in the triangular prism and fill to top capacity.

There are different types of triangles.

There are several formulas that we can use depending on shape of base.

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek *iso* (same) and *skelos* (leg).

**I WOULD ASSUME THAT THE TWO SIDES ARE 4 AND 7 AND THE HEIGHT IS 11. YOU STATED THE FOLLOWING QUESTION.**

A triangular prism has a right triangle base with one leg 4 inches and the other leg 7 inches. The height of the prism is 11 inches. What is its volume?

ANSWER:

**VOLUME = TRIANGULAR BASE X HEIGHT**

**VOLUME = 1/2 X A X C X H **

**VOLUME = 1/2 x 1.9364916731 in x 7 in x 11 in**

**VOLUME =0.5 x 1.9364916731 in x 7 in x 11 in**

**VOLUME = 74.55 in²**

HOW DID WE FIND THE TRIANGULAR BASE?

WE DID NOT KNOW A OR HEIGHT OF TRIANGLE

**Hint:**

**The above is a right triangle**

**The formula is a²+b²=c²**

You are looking for a

or

You are looking for h

You must find height of isosceles triangle and that is one leg of right triangle

The base is 3.5

The hypotenuse is 4

a or h or leg was 1.9364916731

**YOUR QUESTIONS ANSWER**

**74.55 in²**