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