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# Solving algebra equations and problems

In general, the area of a rectangular shape is found by multiplying the length of the area by the width of the area. This can be represented by the formula area = length x width or A = L x W. If you were to measure the length and width in feet, then the result of this equation will be in square feet (ft^2). The resulting number represents the total number of one foot by one foot, or one square foot, units of material you would need to complete the job.

Using the basic formula for rectangular area, determine the area of two different rooms in your house or office in square feet. How did you go about measuring the dimensions of these rooms? Be sure to show your work.

Not all areas are rectangular. Using your book or another resource, look up the formulas for the areas for several different shapes (circle, triangle, trapezoid, etc.). How do these formulas compare to the rectangular area formula you used earlier? Find an example of each shape in your home or office and use the formulas you found to find their areas. Be sure to show your work.

The surface area of a solid object involves the use of derivatives of the formulas you've already found. Look up the formulas for the surface areas of a sphere, a cylinder, and a cone. How do these formulas compare to those you've already used? Find examples of each shape and try these formulas out for yourself. Be sure to show your work.

In general, what can you say about the usefulness of these area formulas? What other methods could be used to find the area and surface areas of objects?

#### Solution Preview

Using the basic formula for rectangular area, determine the area of two different rooms in your house or office in square feet. How did you go about measuring the dimensions of these rooms? Be sure to show your work.

Measuring with a tape measure

Bedroom
Length = 10feet, width = 15feet, Area = 150 ft2

Office
Length = 8feet, with = 10feet, Area = 80ft2

Not all areas are rectangular. Using your book or another resource, look up the formulas for the areas for several different shapes (circle, triangle, trapezoid, etc.). How do these formulas compare to the rectangular area formula you used ...

#### Solution Summary

Using formulas to solve areas of rectangles, circle, triangles, and equilateral triangle and applying the procedure to familiar items.

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