Question

The volume of prism having its base a right angled triangle is 864cm^3.if the length of the sides containing the right angle are 6cm and 8cm calculate the height of the prism.​

Answer 1

height: 36 cm

Explanation:

volume of triangle prism = 0.5 * base * altitude * height

using the formula:

0.5 * 8 * 6 * height = 864

24 * height = 864

height = 864/24

height = 36 cm

Answer 2

36 cm

Explanation:

volume of a triangular prism = area of triangle x height of prism

area of triangle = 1/2 x base x height

Therefore, given the perpendicular sides of the triangle are 6 cm and 8 cm, the area of the triangle is:

⇒ area of triangle = 1/2 x 6 x 8 = 24 cm²

If the volume of the prism is 864 cm³:

⇒ 864 = 24 x height of prism

⇒ height = 864 ÷ 24 = 36 cm