Problem 29
Question
Use Heron's formula to find the area of each triangle. Round to the nearest square unit. \(a=11\) yards, \(b=9\) yards, \(c=7\) yards
Step-by-Step Solution
Verified Answer
The area of the triangle is 33 square yards.
1Step 1: Compute the Semi-Perimeter
Calculate the semi-perimeter \(s\) using the formula \(s = \frac{a+b+c}{2}\). Substituting the given side lengths, we get \(s= \frac{11+9+7}{2} = \frac{27}{2} = 13.5\) yards.
2Step 2: Calculate the Area Using Heron's Formula
Now, substitute the values of \(s, a, b, c\) into Heron's formula: Area = \(\sqrt{s(s - a)(s - b)(s - c)}\). That gives us, Area = \(\sqrt{13.5(13.5 - 11)(13.5 - 9)(13.5 - 7)} = 32.811 \, square \, yards\). After rounding to the nearest unit, we get the area as 33 square yards.
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