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Chapter 5: Problem 33

Use Heron's Area Formula to find the area of the triangle. $$a=8, \quad b=12, \quad c=17$$

Short Answer

Expert verified
The area of the triangle using Heron's Formula is approximately 47.93 square units.

Step by step solution

01

Compute the Semi-Perimeter

The semi-perimeter of the triangle is given by \((a+b+c)/2\). Substitute the given side lengths into the formula to find the semi-perimeter. So, \(s = \frac{{8+12+17}}{2} = 18.5\).
02

Apply Heron's Formula

Heron's formula for the area of a triangle is given by \(\sqrt{s(s-a)(s-b)(s-c)}\), where \(s\) is the semi-perimeter of the triangle and \(a, b,\) and \(c\) are the side lengths of the triangle. Substitute the values of \(s, a, b,\) and \(c\) obtained from Step 1 into Heron's formula to calculate the area of the triangle. So, \(Area = \sqrt{18.5(18.5-8)(18.5-12)(18.5-17)}\).
03

Compute the Area

Carry out the multiplication in the expression obtained in step 2 and then take the square root of the resulting product to get the area of the triangle. So, \(Area = \sqrt{18.5 \times 10.5 \times 6.5 \times 1.5}\).

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