Looking at our triangular prism, we can see that the base is an equilateral triangle. We know that altitude h' of the triangle divides it into two 30°- 60°- 90° triangles, where the height of the triangle is given by h'=sqrt(3)*shorter leg
As we can see in previous figure the length of the shorter leg is equal to 3cm. Therefore, we can calculate the height of the triangle.
h'=sqrt(3)*shorter leg ⇔ h'=sqrt(3)* 3
Once we have the altitude h'=3sqrt(3)cm and the base b=6cm, we will find the area of the base using the formula for area of a triangle.
Now the volume of a prism can be calculated using the following formula.
V=Bh
Since we know that the area of the base is B=9sqrt(3)cm^2 and the height is h=18cm. Let's substitute these values into the formula and solve for V.
