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Chapter 5: Problem 39

Use Heron's Area Formula to find the area of the triangle. $$a=2.5, \quad b=10.2, \quad c=9$$

Short Answer

Expert verified
The area of the triangle is approximately \(11.18\) square units.

Step by step solution

01

Finding the semi-perimeter

The semi-perimeter of the triangle (s) can be calculated by adding all the sides of the triangle and then dividing the sum by 2.\nSo, \(s = \frac{{(a + b + c)}}{2} = \frac{{(2.5 + 10.2 + 9)}}{2} = 10.85\)
02

Calculating the area

Next, substitute the values of \(a\), \(b\), \(c\), and \(s\) into Heron's Formula.\nThe area \(A\) is given by \(A = \sqrt{{s(s - a)(s - b)(s - c)}} = \sqrt{{10.85(10.85 - 2.5)(10.85 - 10.2)(10.85 - 9)}}\). The resulting area after carrying out the multiplication is \(A \approx 11.18\) square units.

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