Problem 27 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The area of the triangle is approximately 22 square meters.

Step 1: 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\(s = (14+12+4) / 2 = 15\)

Step 2: 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\ \(A = \sqrt{15 * (15 - 14) * (15 - 12) * (15 - 4)}\)

Step 3: Simplify the expression

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

Step 4: 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.