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Chapter 5: Problem 42

Use Heron's Area Formula to find the area of the triangle. $$a=3.05, \quad b=0.75, \quad c=2.45$$

Short Answer

Expert verified
The area of the triangle is approximately 1.08 square units.

Step by step solution

01

Compute the semi-perimeter

First, you calculate the semi-perimeter of the triangle using the formula \(s = (a + b + c) / 2\). Plugging in our given side lengths, you get \(s = (3.05 + 0.75 + 2.45) / 2 = 3.125\).
02

Apply Heron's Area Formula

Next, you substitute the values into Heron's formula: \(A = \sqrt{s(s - a)(s - b)(s - c)}\), yielding \(A = \sqrt{3.125(3.125 - 3.05)(3.125 - 0.75)(3.125 - 2.45)}\).
03

Evaluate the Expression

Finally, you perform the calculations in the square root to find the area. This would result into the area being approximately equal to 1.08 square units.

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