Notes Surface Area
How Do You Find the Surface Area of 3-Dimensional Figures?
You can use models or formulas to find the surface area of prisms, cylinders, and other 3-dimensional figures.
Like the area of a plane figure, the surface area of a 3-dimensional figure is measured in square units.
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The total surface area of a 3-dimensional figure is equal to the sum of the areas of all its surfaces.
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The lateral surface area of a 3-dimensional figure is equal to the sum of the areas of all its faces and
curved surfaces. It does not include the areas of the figure’s bases.
1.
One way to compute the surface area of a 3-dimensional figure is to use a net of the figure. A net of a
3-dimensional figure is a 2-dimensional drawing that shows what the figure would look like if it were
unfolded, with all its surfaces laid flat. Use the net to find the area of each surface.
2.
You can also find the surface area of a 3-dimensional figure by using a formula. Substitute the dimensions
of the figure in the formula and compute its surface area. The formulas for the total surface area and lateral
surface area of several types of 3-dimensional figures are included in the Mathematics Chart.
Formulas Surface Area
Cube
S = 6s 2
Prism (Lateral)
S = Ph
Prism (Total)
S = Ph + 2B
Pyramid (Lateral)
S = ½ Pl
Pyramid (Total)
S = ½ Pl + B
Cylinder (Lateral)
S = 2rh
Cylinder (Total)
S = 2rh + 2r or S = 2r(h + r)
2