How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 31 units in length?

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How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 31 units in length?

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Answer 1 · 2015-12-26T00:35:36

Substitute the values into Heron's formula to find:

$A = \sqrt{109956} \approx 331.59614$ $A = sqrt(109956) ~~ 331.59614$

Explanation:

Heron's formula can be written:

$A = \sqrt{s p (s p - a) (s p - b) (s p - c)}$ $A = sqrt(sp(sp-a)(sp-b)(sp-c))$

where $A$ $A$ is the area, $a$ $a$ , $b$ $b$ , $c$ $c$ are the lengths of the sides and

$s p = \frac{a + b + c}{2} X$ $sp = (a+b+c)/2 color(white)(X)$ is the semi-perimeter.

In our example, $a = 25$ $a=25$ , $b = 28$ $b=28$ , $c = 31$ $c=31$

$s p = \frac{a + b + c}{2} = \frac{25 + 28 + 31}{2} = \frac{84}{2} = 42$ $sp = (a+b+c)/2 = (25+28+31)/2 = 84/2 = 42$

$A = \sqrt{s p (s p - a) (s p - b) (s p - c)}$ $A = sqrt(sp(sp-a)(sp-b)(sp-c))$

$= \sqrt{42 (42 - 25) (42 - 28) (42 - 31)}$ $=sqrt(42(42-25)(42-28)(42-31))$

$= \sqrt{42 \cdot 17 \cdot 14 \cdot 11}$ $=sqrt(42*17*14*11)$

$= \sqrt{109956} \approx 331.59614$ $=sqrt(109956) ~~ 331.59614$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 31 units in length?

1 Answer

Explanation:

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