**Solving problems involving lateral & surface are of rectangular/triangular prisms and pyramids**

difference between lateral & total

surface area

Lateral means "on the sides", so the lateral surface area would be the surface area on the sides of your figure. Lateral does not include the base or bases of your figure.

Rectangular Pyramid

To find the surface area of a rectangular pyramid, you have to find the base first, (unless you're doing lateral surface area) which is the square or rectangle in the center by multiplying the length times the width. Then find the area of the triangles on the side. If theyre all the same, find one and multiply by four. If its two different sizes, find one and multiply by 2 and do the same with the other length (the shapes that are opposite from one another are the same length). After you're done, add up your triangles with your base to find the answer.

Triangular Prism

To find the surface area of the triangular prism, like i said, i recommend doing the bases first. The bases are two triangles on each side. Find the area and since there is two, multiply it by two. After that, look at the rectangle with the triangles on the top and bottom of it. Multiply the length times the width. Then look at the two other rectangles and find the area of one, then multiply by two since they will be the same size.

Note: when finding the area of a triangle, multiply the height times the base then divide it by two,

The total surface area would be the entire surface area, including the bases for a rectangular or triangular pyramid or prism.

Rectangular prism

To find the surface area of a rectangular prism, you have to find all of the lengths. First, i recommend finding the bases, or top and bottom, first (unless its lateral surface area). You have to multiply the length times the width of the bases and since there is two, multiply it by two.

Next, find a side and do the same thing-multiply the length times the width, and since there is two, multiply it by two.

After that, do the same thing with the other side. When you are done, add up all the sides.

Note: If it is only lateral, don't do the bases. :)

Triangular pyramid

To find the surface area of a triangular pyramid, you have to find the area of the base first (unless doing lateral surface area). The base is a triangle so you have you multiply the height by the base and divide by two. If its an equilateral triangle, you can multiply the area of the base by four so you have all four triangles. if its not, find the area of the side triangles by finding one and multiplying by three. Then add the area of the three side triangles to the area of the base.