Math help please?

Question

hi i really need help for this question


the square base of a pyramid has side lengths of 6 cm. Each triangluar face has a height of 10 cm.

a) determine the surface area of the pyramid --- i tried and i got 160 but the book says it's not right can someone help me

b) determine the surface area of the pyramid if the side lengths and height are doubled

c) determine the surface area of the pyramid if the side lengths and height are tripled

d) compare you answers for parts, a, b, c what do you notice.

Answer 1

a) surface area is just the sum of the surface area of each traingle + square base
Area of square base = 6x6 = 36 cm^2
Area of 4 Triangles = 4 x 1/2 x base x height = 2 x 6 x 10 = 120
Surface Area of the Pyramid = 36 + 120 = 156

b)
Area of square base = (12)(12) = 144
Area of 4 Triangles = 2 x 12 x 20 = 480
Surface area of Pyramid = 624

c) base = (18)(18) = 324
4 triangles = 2 x 18 x 30 =1080
pyramid = 1404

d) 156, 624, 1404
as the side and length doubles, the surface area increases but at a decreasing rate.
At first it increased by 4 times
Second, it only increased about 2 times

Answer 2

I found a formula that says the surface area is 1/2 ps where p is the base perimeter and s is the slant height, which I assume is the height of the triangular face. That would make the answer for a 120. Is that correct?

You can use the same info for the other parts.

Answer 3

The area of each face is .5*h*b, where h is the height and b the length of the base. There are four faces. The total area is not 160.

If you look at the formula: total face area = 2*a*b, you can tell what happens if you double or triple both a and b.