how do you find the surface area of a square pyramid?

Answer 1

ok. first, find the area of the square, by multiplying the base, x, by itself. so that is equal to x * x = x squared.

then, you need to find the area of each of the triangles on the outside.

to do this, you need to know the height of the pyramid. then, you use this height y, to find the height of the triangles making the outside of the pyramid.

you can do this by finding the hypotenuse of the triangle formed when you draw a point from the side of the base to the center. the distance is clearly x/2. so now you have a triangle with base x/2 and height of y.

so, the hypotenuse of this triangle is the:
square root of (x/2) squared + (y) squared= z

now, z is the height of the triangles making up the face of the pyramid. to find their areas, simply find the area of one and multiply by 4. to find the area of one, you need the formula for the area of a triangle which is base * height * 1/2 or (base * height) / 2

so, you have height z and base x for the triangles that make up the face of the pyramid. so, each area is equal to:

z * x * 1/2

then you multiply this by 4 and add the area of the base:

4(z*x*1/2) + (x) squared = 2zx + (x) squared

Answer 2

a square pyramid is made up of a square and 4 triangles . The area of the square base is = to side squared or sto the power of 2. The other part is 4 times the area of the triangle Area of triangle = 1/2 base time height. Add the area of the square and the 4 triangles and you are done

Answer 3

It depends on what information you have. The lateral faces are four congruent triangles, and I presume you know how to find the area of one triangle. Do that for one lateral face and multiply it by four. If you're including the base, then just add in that area.

How you find the area of the faces is the place where we'd need to know what information you're given. What you need is the length of the base and the slant-height of the pyramid. If you have those, you're good to go. If you have something else, then you'll need to figure those out.

I can give a more specific answer if you give me more specifics.

Answer 4

http://ca.answers.yahoo.com/question/index?qid=20061229104721AAwwfBH

http://www.pwcs.edu/i-tech/TLCF/formulas/SASquarePyr2.htm