Question

How do you solve surface area

Answer 1

For squares and rectangles, it's easy: multiply the length of one side by the other.

For equilateral and isosceles triangles, measure the height (distance from one pointy tip to the point exactly halfway between the other two pointy tips) and multiply by half of the width of the base.  Scalene triangles are more complicated and vary depending on their exact measurements.  However, you can often divide them into several smaller isosceles triangles that can be easily calculated for.

For cylinders, find the area of one circle (use the equation $A = \pi r^{2}$) and multiply the answer by 2.  Call this number A.  Then, find the circumference of one of the circles.  Call this number C.  Then, measure the length of the cylinder.  Call this number L.  Multiply L and C together, then add A to the product.  That's the surface area of the cylinder.

For spheres, use the equation $A = 4 \pi r^{2}$, where A represents the surface area, $\pi$ is approximately equal to 3.14, and r represents the radius, which is always exactly half of the diameter. 

Most other shapes, whether 3-dimensional or 2-dimensional, can be calculated by simply adding together the areas of their component parts.  An octagon can be divided into 8 isosceles triangles, which if you're given the right information are easy to calculate for (height times base divided by 2).  Once you find the area of one piece of the octagon, multiply by 8 (the number of sides).  This works for any regular polygon of n sides.
 
If you're being given irregular shapes, just divide them into many smaller, simpler ones that you already know how to calculate for.  Once you've determine the area of each of the component parts, add everything together to find the total area of the whole.