Question

find the lateral area, volume and total area

Answer 1

Alrighty let's see the picture

Answer 2

This is a hexagonal pyramid. Lateral Area of that is:

\[3a \sqrt{h^2+\frac{ 3a^2 }{ 4 }}\]

Where a is base edge and h is the height

Answer 3

ok one sec let me solve

Answer 4

I think in the diagram, the 6 looks like it is the height of the triangle and not the height of the pyramid. If that is the case, all you have to do is find the area of one triangle and multiply it by 6 to get the lateral surface area.

Answer 5

really?!

Answer 6

so 72?

Answer 7

Well, if I take 6 to be the height of the triangle, then the area of one triangle = 1/2 * base * height = 1/2 * 4 * 6 = 12. Multiply that by 6 for the six triangles and you get 72 as the lateral surface area. If that is wrong then you can try the above formula by marissa.

Answer 8

no its right! now i need the volume? and total area

Answer 9

marissa u still there?

Answer 10

For the total area just add the area of the hexagon base to the lateral surface area.

Answer 11

how do u find the area of a hexagon?

Answer 12

Area of hexagon = \(\Large \frac {3\sqrt{3}}{2}a^2\) where 'a' is the side of the hexagon.

Answer 13

how does it come out to be in the form of __+__ square root _?

Answer 14

Put a = 4 in the above formula to calculate the area of the hexagonal base. To that add 72, the lateral surface area calculated earlier.

Answer 15

3 squareroot 3 over 32?

Answer 16

put a = 4: \(\Large \frac {3\sqrt{3}}{2}a^2 = \frac {3\sqrt{3}}{2}16 = 24\sqrt{3}\).
Total surface area = \(\Large 72 + 24\sqrt{3}\)

Answer 17

how u get 24?

Answer 18

a = 4, a^2 = 16. divided by 2 is 8. multiplied by 3sqrt(3) = 24sqrt(3).

Answer 19

o got it!!! thank u! so how do i find the volume?

Answer 20

Volume of a pyramid = 1/3 * area of base * height of the pyramid.

Answer 21

so \[ 24\sqrt{3}*6\]?

Answer 22

1/3 * 24 * sqrt(3) * height of the pyramid.
You have to use Pythagoras theorem to find the height of the pyramid. The 6 in the diagram is the height of the triangle and not the height of the pyramid.

Answer 23

o ok thank you

Answer 24

You are welcome.