Question

Solve the problem. Find the surface area of a right regular hexagonal pyramid with sides 2 cm and slant height 5 cm. Round youranswer to the nearest hundredth.​

Answer 1

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 = $\sqrt[3]{3}\times s^{2}$

                            = $\sqrt[3]{3}\times 2^{2}$

On solving we get:

Area of the base(b) = $20.784$

Then, we find the perimeter(p) :

Perimeter = s × 6

$p=2\times 6=12$

Now, putting the formula for getting the surface area:

Surface area = perimeter × height/2 + Area of the base.

$SA=\frac{p\times h}{2}+b$

$SA=\frac{12\times 5}{2}+20.784$

$SA=30+20.784$

$SA=50.784$

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.