Answer:
The surface area of the right regular hexagonal pyramid is 50.78 cm².
Step-by-step explanation:
Given:
A right regular hexagonal pyramid with sides(s) 2 cm and slant height(h) 5 cm.
Now, to find the surface area(SA) of the right regular hexagonal pyramid.
So, we find the area of the base(b) first:
Area of the base = [tex]\sqrt[3]{3}\times s^{2}[/tex]
= [tex]\sqrt[3]{3}\times 2^{2}[/tex]
On solving we get:
Area of the base(b) = [tex]20.784[/tex]
Then, we find the perimeter(p) :
Perimeter = s × 6
[tex]p=2\times 6=12[/tex]
Now, putting the formula for getting the surface area:
Surface area = perimeter × height/2 + Area of the base.
[tex]SA=\frac{p\times h}{2}+b[/tex]
[tex]SA=\frac{12\times 5}{2}+20.784[/tex]
[tex]SA=30+20.784[/tex]
[tex]SA=50.784[/tex]
As, the surface area is 50.784 and rounding to nearest hundredth becomes 50.78 because in hundredth place it is 8 and in thousandth place it is 4 so rounding to it become 50.78.
Therefore, the surface area of the right regular hexagonal pyramid is 50.78 cm².
