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Chapter 7: Problem 28

Use Heron's formula to find the area of each triangle. Round to the nearest square unit. \(a=16\) meters, \(b=10\) meters, \(c=8\) meters

Short Answer

Expert verified
The area of the triangle is \(30\) square meters.

Step by step solution

01

Calculate the semi-perimeter of the triangle

First, calculate the semi-perimeter of the triangle, s. Use the formula \(s = \frac{a + b + c}{2}\) with \(a = 16\) meters, \(b = 10\) meters, and \(c = 8\) meters. Plug these values in the formula and solve for \(s\),\(s = \frac{16 + 10 + 8}{2} = 17\) meters.
02

Apply Heron's formula to calculate the area of the triangle

Using the derived semi-perimeter value, apply Heron's formula to calculate the area of the triangle. The formula is Area \(= \sqrt{s(s - a)(s - b)(s - c)}\)Plug in the given values \(s = 17\), \(a = 16\), \(b = 10\), \(c = 8\), Area \(= \sqrt{17(17 - 16)(17 - 10)(17 - 8)} = 30\) square meters.

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