Respuesta :
The height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
What is a pyramid that has a hexagonal base?
The pyramid has a hexagonal base with six isosceles triangular faces known as a hexagonal base pyramid. It is also called a heptahedron.
We have,
The length of the base edge of a pyramid = x units
The height of the pyramid is three times longer than the base edge ie.
The height of the pyramid = 3x
The area of an equilateral triangle with base length x units is [tex]\rm x\sqrt{3}[/tex] square units square(let's assume)
Then the area of the hexagon base = 6×[tex]\rm x\sqrt{3}[/tex] ⇒ 6[tex]\rm x\sqrt{3}[/tex] square units.
Because the hexagon base has a six-equilateral triangle.
Let's assume the area of a hexagonal base is Y times the equilateral triangle.
[tex]\rm 6x\sqrt{3} = Y \times x\sqrt{3}[/tex]
Y = 6 times
We know the volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2} a^2h[/tex]
Where a is the base length and h is the height of the hexagonal pyramid.
Here a = x units and h = 3x units
Then Volume:
[tex]\frac{\sqrt{3} }{2} x^2(3x)\\\\\frac{{3} }{2} \sqrt{3}x^2[/tex]
Thus, the height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
Learn more about the pyramid here:
https://brainly.com/question/17615619
