Question

HIJK is a triangle based pyramid. The base HIJ is an equilateral triangle with side 10cm. The volume of the pyramid is 300cm^3. Calculate the perpendicular height, h, of the pyramid.

Answer 1

20.78 cm^3 to the nearest hundredth.

Explanation:

Volume = 1/3 * a * h where a = area of triangular base and h = the height.

The area of the triangle

= 1/2 * base * height

Its height = √(10^2-5^2)

= √75.

So its area = 1/2 * 10 * √75

= 5√75

So for the pyramid we have:

300 = 1/3 * 5√75 * h

h = 300 / (1/3 * 5√75)

= 20.78 cm^3.