Respuesta :
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 = [tex]\frac{1}{2}\times{\text{Area of Base}\times{\text{Height}[/tex]
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=[tex]\frac{\sqrt3}{4}\times(Side)^2=\frac{\sqrt3}{4}\times(4)^2=4 \sqrt3[/tex] cm²
So, Area of three triangle which are faces of pyramid = (12 - 4 √3)cm²
Area of triangle = [tex]\frac{1}{2} \times (Base)\times(Height)[/tex]
12 - 4 √3= [tex]\frac{1}{2} \times (4)\times(Height)[/tex]
Height =[tex]\frac{12-4\sqrt3}{2}[/tex]
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
The volume of the pyramid with the base as an equilateral triangle is 16 cm³ if the base area is 12 cm², and the height of the pyramid is 4 cm.
What is a pyramid with an equilateral triangle?
In geometry, it is defined as the shape having an equilateral triangle with equal sides length and if we rotate the pyramid it will look the same.
We have:
The base length of the equilateral triangle = 4 cm
Area of the base = 12 cm²
We know the volume of the pyramid with the base as an equilateral triangle is given by:
[tex]\rm V = \frac{1}{3} bh[/tex]
Here b is the base area of an equilateral triangle and
h is the height of an equilateral triangle
We have b = 12 cm², and h = 4 cm
Put these values in the formula, we get:
[tex]\rm V = \frac{1}{3} \times4\times12[/tex]
V = 16 cm³
Thus, the volume of the pyramid with the base as an equilateral triangle is 16 cm³ if the base area is 12 cm², and the height of the pyramid is 4 cm.
Learn more about the pyramid here:
brainly.com/question/13057463
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