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Chapter 7: Problem 27

Use Heron's formula to find the area of each triangle. Round to the nearest square unit. \(a=14\) meters, \(b=12\) meters, \(c=4\) meters

Short Answer

Expert verified
The area of the triangle is approximately 22 square meters.

Step by step solution

01

Calculate semi-perimeter

Using the formula \(s = (a+b+c)/2\), substitute the given values of a, b, and c to get the semi-perimeter:\n\(s = (14+12+4) / 2 = 15\)
02

Substitute values into Heron's formula

Using Heron's formula \(A = \sqrt{s(s - a)(s - b)(s - c)}\), substitute the values of s, a, b, and c:\n\ \(A = \sqrt{15 * (15 - 14) * (15 - 12) * (15 - 4)}\)
03

Simplify the expression

Simplify the expression to find the area of the triangle:\n \ \(A = \sqrt{15 * 1 * 3 * 11} = \sqrt{495}\)
04

Approximate the square root

Since the area should be given in whole numbers, approximate the value of \(\sqrt{495}\) to the nearest whole number:\nA = 22.

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