How do I solve these?

Question

I need to figure the volume and surface areas of both of these...

A pyramid with base of 6x6 and slant height of 5. Volume? Surface area I know is 96yards squared.

"stairs". 7cm base, 1cm high, 1cm across. Right behind it 7cm base, 2cm highter than previous, 2cm across. Then a 7cm base that is 2cm higher than previous, with another across of 2cm. HOPING that made sense.... surface area? It's hard because they're all next to each other. What about volume?

Answer 1

Let

b = length of side of base
h = slant height
S = surface area including base
V = Volume
w = vertical height of pyramid

We have

S = b² + 4[(1/2)bh] = 6² + 2*6*5 = 36 + 60 = 96 yards²

To find the volume we need the vertical height of the pyramid.

V = ⅓b²w

The vertical height can be determined using the Pythagorean Theorem. The vertical height is the perpendicular from the vertex at the top to the center point of the base.

w = one leg
b/2 = second leg
h = hypotenuse

w² = h² - (b/2)² = 5² - (6/2)² = 25 - 9 = 16
w = 4 yards

V = ⅓b²w = ⅓(6²)(4) = ⅓(36)(4) = 48 yards³

Answer 2

The surface area would be lxbxh (length,breath,height all multiplied together)

As to volume they would have given you more infomation but if you want you can work it out once you have gotten your surface area.

Make sense??? hope it helps goodluck