GA - Surface Area Lesson

Surface Area

The surface area of a solid figure is the sum of the areas of all exposed sides of a figure. You can calculate the area of a figure by finding the areas of all of its faces and adding them. In sixth grade, you learned to calculate surface area using a net, or a two-dimensional representation of all sides of a solid. In this lesson, you will find the surface areas for right prisms and composed figures.

Let us start with basic shapes just as we did in the previous lesson.

Start with a rectangular prism:

Rectangular prism with measurements 7 in, 7 in, 12 in

Use the formula 2lw +2lh+2wh insert the dimensions

S =2(7x7)+2 (7x12)+2(7x12)

S=2(49)+2(84)+2(84)

S=434 equation image indicator LaTeX: in^2 $in^2$

Try it with a triangular prism:

Triangular prism with measurements 22m, 13m, 11m, and height of 8m

Use the formula S=2B+Ph

B is the area of the base, P is the perimeter of the bases, and h is the height of the prism.

S =2( equation image indicator )+(13+13+8)*22

S = 88+(34)*22

S = 88 + 748

S=836 equation image indicator LaTeX: m^2 $m^2$

We can easily find the surface area of a cube by using the same formula as a rectangle:

cube with measurements 6m, 6m, 6m

2(6x6) + 2(6x6) + 2(6+6)

72 + 72 + 72 =216 equation image indicator LaTeX: ft^2 $ft^2$

Composed shapes for surface area are tricky because, after you find the surface area of each shape, you must remember to subtract those sides whose sides are not exposed.

Look at the example below to see how this is done.

composed image with measurements 10ft, 14ft, 8ft, 4ft, 6ft, 10ft, 6ft

As you have learned, it is simple to calculate area and volume of composed figures when you break apart the shapes, so the same rule applies to surface area. Let's find the surface area of the large prism first.

2(6 x 10) + 2(10 x 14) + 2(14 x 6)

2(60) + 2(140) + 2(84)

120 + 280 + 168 = 568 square ft

Next, find the surface area of the small prism.

2(4x8)+2(4x10)+2(8x10)

2(32)+2(40)+2(80)

64+80+160 = 304 square ft

We are not finished. Remember, we are looking for surface area, so there are spaces that are not exposed and that overlap. How much overlapping surface area must we subtract?

2(8 x 10) One side from the large prism and one side from the small prism.

2(80) = 160 square ft

The surface area of this composed figure is: 568 + 304 - 160 = 712 square ft.

Surface Area Practice

Surface Area Homework

Now that you have spent some time learning strategies for solving problems with surface area, you are ready to complete your Geometric Applications: Surface Area Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key. Links to an external site.

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