wat is the formula for the total surface area of a pyramid ?

Answer 1

a^2+ax {root under(4h^2+a^2)}

a=length of base
h= height
only for squared pyramid

Answer 2

If it's a tetrahedral pyramid (four faces all being equilateral triangles):
Let 's' be the length of one of the sides. The area of a triangle is half the base times the height. The height cuts an equuilateral triangle into two right triangles. You can use the Pythagorean Theorem (a^2 + b^2 = c^2) to determine the length of this height:
( 1/2 * s )^2 + b^2 = ( s )^2,
b^2 = s^2 - 1/4*s^2,
b^2 = 3/4 * s^2,
b = sqrt(3)/2 * s.

So the area of one of the faces is (1/2)(s)(s*sqrt(3)/2).
There are four faces so your formula is:
A = s^2 * sqrt(3).

For a pyramid with a square base:
Let 's' be the length of the base. This means s^2 is the area of the base.
Let 'h' be the height of the pyramid. You'll need to determine the length of one of the ascending edges. A triangle can be formed by the pyramid's height, one of the ascending edges, and the line segment formed by the point directly below the peak and one of the base corners. That line segment is half the diagonal of the base. The diagonal can be determined by the Pythagorean Theorem:
s^2 + s^2 = d^2,
d = sqrt(2 * s^2),
d = s*sqrt(2).
So the line segment is 1/2*s*sqrt(2).
Use the Theorem again to find the length of the ascending edge, 'e':
(1/2*s*sqrt(2))^2 + h^2 = e^2,
e = sqrt(1/2*s^2 + h^2).
Ummm, sorry, we're going to use the Theorem one more time to determine the height (call it 'x') of one of the triangular faces of the pyramid:
e^2 = (1/2*s)^2 + x^2,
1/2*s^2 + h^2 = 1/4*s^2 + x^2,
x^2 = 1/4*s^2 + h^2,
x = sqrt(1/4*s^2 + h^2).
There, use the half-base-times-height formula and multiply it by 4 and add it to the area of the base to get your final answer:
1/2*s*sqrt(1/4*s^2 + h^2)*4 + s^2,

A = 2*s*sqrt(1/4*s^2 + h^2) + s^2.

I'm fairly sure that's correct.

Feel free to email me for any clarifications.

Answer 3

That depends on the pyramid. For each face (a triangle), you would need to know the height and base dimensions, and use the area formulas for triangles. Depending on whether or not a pyramid has three or four sides, the base will be either a triangle or rectangle, and you can use the appropriate surface area equations there.

In general, the surface area of a pyramid is
Area = (number of faces)*(area of each face) + (area of base)

Answer 4

The Formula is (1/3) X (base area) X (Height). That is the general formula..Look carefully before answering Cos sOmetiMes, the qUestions maY be oUt to Trick yOu...Good Luck....

Answer 5

What kind of pyramid? Is every face bounded by the same number of sides -- are they, for example, all triangles? Are all the faces alike, or are some larger than others?

Answer 6

The first link below will give you the area equation you seek. The second link is to the home page for the Wolfram Mathworld site.
It's a great site for math questions.

Answer 7

it is for the surface : (base X height)/2

for the volume : (base area X height)/3