The height of a triangular prism is 6 cm and its base is a triangle with an area of 12 cm². What is the volume of the prism in cubic centimeters?
To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism.
First, calculate the area of the base triangle which is 12 cm². Let's assume the base triangle has a base of b cm and a height of h cm.
Area of a triangle = 1/2 * base * height
12 = 1/2 * b * h
24 = b * h
Now let's find the height of the base triangle given that its base is unknown but we know the height of the prism is 6 cm. Since the prism is a triangular prism, the height of the prism is the same as the height of the base triangle. Therefore, h = 6 cm.
Substitute h = 6 cm into the equation 24 = b * h, we get:
24 = b * 6
b = 24 / 6
b = 4 cm
Now that we know the base triangle has a base of 4 cm and a height of 6 cm, we can find the volume of the prism.
Volume of a triangular prism = area of base * height of prism
Volume = 12 cm² * 6 cm
Volume = 72 cm³
Therefore, the volume of the triangular prism is 72 cubic centimeters.