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Chapter 5: Problem 38

Use Heron's Area Formula to find the area of the triangle. $$a=33, \quad b=36, \quad c=25$$

Short Answer

Expert verified
The area of the given triangle using Heron's area formula is 396 square units.

Step by step solution

01

Compute the Semi-Perimeter

First, calculate the semi-perimeter 's' of the triangle which is the sum of the three sides divided by two. 's' = \((a + b + c)/2 \Rightarrow s = (33 + 36 + 25)/2 = 47\).
02

Substitute in Heron's Formula

Now, use Heron's formula to find the area. The formula is given by \(A = \sqrt{s(s - a)(s - b)(s - c)}\). Substitute the computed 's', 'a', 'b' and 'c' in the formula: \(A = \sqrt{47(47 - 33)(47 - 36)(47 - 25)}\).
03

Perform the Computation

Solving the above equation we get \( A = \sqrt{47*14*11*22} = 396 \, square \, units\). Thus, the area of the triangle is 396 square units.

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