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Chapter 5: Problem 43

Use Heron's Area Formula to find the area of the triangle. $$a=1, \quad b=\frac{1}{2}, \quad c=\frac{3}{4}$$

Short Answer

Expert verified
The area of the triangle is approximately 0.161 square units.

Step by step solution

01

Calculate the semi-perimeter

The semi-perimeter or 's' of the triangle is given by the formula \( s = (a + b + c) / 2 \). Substituting the values of sides a, b and c into the formula, we get \( s = (1 + 0.5 + 0.75) / 2 = 1.125 \).
02

Apply Heron鈥檚 formula

The area 'A' of the triangle can now be found by substituting the values of a, b, c and s into Heron鈥檚 formula: \( A = \sqrt{s(s - a)(s - b)(s - c)} \). Substituting the values of sides a(1), b(0.5), c(0.75) and s(1.125), we get: \( A = \sqrt{1.125(1.125 - 1)(1.125 - 0.5)(1.125 - 0.75)} \).
03

Simplify and solve

To obtain the area, we simplify the above expression. This results in an approximately numerical value of the area \( A \). Let's calculate: \( A = \sqrt{1.125(0.125)(0.625)(0.375)} \approx 0.161 \).

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