Answer:
(a)
h=3x
(b)
(c)
(d)
units^3
Step-by-step explanation:
We are given a regular hexagon pyramid
Since, it is regular hexagon
so, value of edge of all sides must be same
The length of the base edge of a pyramid with a regular hexagon base is represented as x
so, edge of base =x
b=x
Let's assume each blank spaces as a , b , c, d
we will find value for each spaces
(a)
The height of the pyramid is 3 times longer than the base edge
so, height =3*edge of base
height=3x
h=3x
(b)
Since, it is in units^2
so, it is given to find area
we know that
area of equilateral triangle is
h=3x
b=x
now, we can plug values
(c)
we know that
there are six such triangles in the base of hexagon
So,
Area of base of hexagon = 6* (area of triangle)
Area of base of hexagon is
(d)
Volume=(1/3)* (Area of hexagon)*(height of pyramid)
now, we can plug values
Volume is
units^3