Question

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

Answer 1

Solution:

Let me define pyramid first.A pyramid is a Polyhedron , whose base  can be any polygon and it's faces are triangular which meet at a point called vertex.

Volume of Pyramid =  $\frac{1}{2}\times{\text{Area of Base}\times{\text{Height}$

Side of base which is an equilateral triangle= 4 cm

Area of whole pyramid = 12 square cm

Area of Equilateral triangle having side 4 cm=$\frac{\sqrt3}{4}\times(Side)^2=\frac{\sqrt3}{4}\times(4)^2=4 \sqrt3$ cm²

So, Area of three triangle which are faces of pyramid = (12 - 4 √3)cm²

Area of triangle = $\frac{1}{2} \times (Base)\times(Height)$

12 - 4 √3= $\frac{1}{2} \times (4)\times(Height)$

Height =$\frac{12-4\sqrt3}{2}$

Height=(6-2√3) cm

Volume of pyramid = Area of Equilateral triangle which is it's Base × Height of Pyramid

          =4√3 × (6-2√3) cm³

           =(24 √3 -24)

           = 24 (1.732-1)

          =24 × 0.732

          =17.568 cm³

Answer 2

The answer would be 16cm^3.

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