Trigonometry For Dummies
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When you know the length of a triangle’s three sides and you don’t know an altitude, you can use Hero’s formula to find the area. Check it out:

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where a, b, and c are the lengths of the triangle’s sides and S is the triangle’s semiperimeter

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Now use Hero’s formula to calculate the area of a triangle with sides of length 5, 6, and 7. First, you need the triangle’s perimeter (the sum of the lengths of its sides), and from that you get the semiperimeter. The perimeter is 5 + 6 + 7 = 18, so you get 9 for the semiperimeter. Now just plug 9, 5, 6, and 7 into the formula:

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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