Problem 46 - Algebra and Trigonometry Real Mathematics, Real People

Question

Use Heron's Area Formula to find the area of the triangle. $$a=\frac{3}{5}, \quad b=\frac{5}{8}, \quad c=\frac{3}{8}$$

Step-by-Step Solution

Answer

The area of the triangle is \(A=\frac{1}{40}\)

Step 1: Find the Semi-Perimeter

First calculate the semi-perimeter (s) of the triangle using the formula \(s=\frac{a+b+c}{2}\). Substitute the given values into this formula: \(s=\frac{\frac{3}{5} + \frac{5}{8} + \frac{3}{8}}{2}\)

Step 2: Simplify the Semi-Perimeter

Simplify the fraction to get the value of s: \(s=\frac{14}{40} = \frac{7}{20}\).

Step 3: Apply Heron's formula

Now, apply Heron's formula \(A=\sqrt{s(s-a)(s-b)(s-c)}\) to find the area of the triangle. Here, \(s=\frac{7}{20}, a=\frac{3}{5}, b=\frac{5}{8}, c=\frac{3}{8}\). Substitute these values into Heron's formula and calculate the result.

Step 4: Simplify the Area

After simplification, the area of the triangle is calculated as \(A=\frac{1}{40}\)