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Chapter 5: Problem 37

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 is 40.5 square units.

Step by step solution

01

Compute Semi-Perimeter (s)

First let's calculate the semi-perimeter of the triangle. This is done with the formula s = (a + b + c) / 2. Substitute the given side lengths a=8, b=12 and c=17 into the formula to obtain \(s = (8 + 12 + 17) / 2 = 18.5\).
02

Apply Heron's Area Formula

In this step, we substitute the semi-perimeter (s), and the lengths of the triangle sides into Heron's formula: A = \[\sqrt{s(s - a)(s - b)(s - c)}\]. Ensuring to substitute the correct value for s results in A = \[\sqrt{18.5(18.5 - 8)(18.5 - 12)(18.5 - 17)}\].
03

Compute the Area

In the final step, perform the calculations inside the square root, before then taking the square root to find the area. So, A = \[\sqrt{18.5 * 10.5 * 6.5 * 1.5}\] which simplifies to A = 40.5 square units.

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