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

The surface area of right regular hexagonal pyramid = 82.222 cm³

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 =
`(3√(3))/(2)* a^(2) + 3 a \sqrt{h^(2)+ 3* (a^(2))/(4)}`

Where a is the base side

And h is the slant height

So, The surface area of right regular hexagonal pyramid =
`(3√(3))/(2)* 3^(2) + 3 * 3 \sqrt{6^(2)+ 3* (3^(2))/(4)}`

Or, The surface area of right regular hexagonal pyramid =
`(3√(3))/(2)* 9 + 9 \sqrt{36+ 3* (9)/(4)}`

Or, The surface area of right regular hexagonal pyramid = 23.38 + 9 ×
`(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