Question

find the surface area of a right regular hexagonal pyramid with sides 3 cm and slant heights 6cm. show all of your work.​

Answer 1

Answer:

The surface area of right regular hexagonal pyramid = 82.222 cm³

Step-by-step explanation:

Given as , for regular hexagonal pyramid :

The of base side = 3 cm

The slant heights = 6 cm

Now ,

The surface area of right regular hexagonal pyramid = $\frac{3\sqrt{3}}{2}\times a^{2} + 3 a \sqrt{h^{2}+ 3\times \frac{a^{2}}{4}}$

Where a is the base side

And h is the slant height

So, The surface area of right regular hexagonal pyramid = $\frac{3\sqrt{3}}{2}\times 3^{2} + 3 \times 3 \sqrt{6^{2}+ 3\times \frac{3^{2}}{4}}$

Or, The surface area of right regular hexagonal pyramid = $\frac{3\sqrt{3}}{2}\times 9 + 9 \sqrt{36+ 3\times \frac{9}{4}}$

Or,  The surface area of right regular hexagonal pyramid = 23.38 + 9 × $\frac{171}{4}$

∴  The surface area of right regular hexagonal pyramid = 23.38 + 9 × 6.538

I.e The surface area of right regular hexagonal pyramid = 23.38 + 58.842

So,  The surface area of right regular hexagonal pyramid = 82.222 cm³ Answer