Question

A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12StartRoot 3 EndRoot cm2. What is the volume of the pyramid?

Answer 1

This question is incomplete. Find attached to this answer the required diagram.

Answer:

16√3 cm³

Step-by-step explanation:

Volume of a pyramid = 1/3 × Base area × Height

The base area is given as 12√3 cm²

But the height is not given

From the attached diagram an angle was given

Using Trigonometric function of Tangent

tan = Opposite/Adjacent

Opposite = Height of the pyramid

Adjacent = base length of the pyramid = 4√3

Hence,

tan 30° = opposite/4√3

Cross multiply

Opposite = tan 30° × 4√3

Opposite = Height of the pyramid = 4 cm

Volume of a pyramid = 1/3 × Base area × Height

= 1/3 × 12√3 × 4

= 16√3 cm³