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Chapter 5: Problem 40

Use Heron's Area Formula to find the area of the triangle. $$a=75.4, \quad b=52, \quad c=52$$

Short Answer

Expert verified
The area of the triangle is approximately 2058.85 square units.

Step by step solution

01

Calculating the Semiperimeter

The first step is to calculate the semiperimeter of the triangle using the formula \(s = (a+b+c) / 2\). Substituting the given side lengths into the formula, we get: \(s = (75.4+52+52) / 2 = 89.7\)
02

Substituting into Heron's Area formula

Next, substitute the calculated semiperimeter \(s\) and the given side lengths \(a, b, c\) into Heron's formula: \[Area = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{89.7 (89.7-75.4)(89.7-52)(89.7-52)}\]
03

Calculating the Area

Finally, calculate the square root value to obtain the area of the triangle: \(Area \approx 2058.85\) square units

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