How do you use Heron's formula to find the area of a triangle with sides of lengths $1$ $1$ , $1$ $1$ , and $1$ $1$ ?

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How do you use Heron's formula to find the area of a triangle with sides of lengths $1$ $1$ , $1$ $1$ , and $1$ $1$ ?

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Answer 1 · 2016-01-25T02:48:59

$A r e a = 0.433$ $Area=0.433$ square units

Explanation:

Heron's formula for finding area of the triangle is given by
$A r e a = \sqrt{s (s - a) (s - b) (s - c)}$ $Area=sqrt(s(s-a)(s-b)(s-c))$

Where $s$ $s$ is the semi perimeter and is defined as
$s = \frac{a + b + c}{2}$ $s=(a+b+c)/2$

and $a, b, c$ $a, b, c$ are the lengths of the three sides of the triangle.

Here let $a = 1, b = 1$ $a=1, b=1$ and $c = 1$ $c=1$

$\Rightarrow s = \frac{1 + 1 + 1}{2} = \frac{3}{2} = 1.5$ $implies s=(1+1+1)/2=3/2=1.5$

$\Rightarrow s = 1.5$ $implies s=1.5$

$\Rightarrow s - a = 1.5 - 1 = 2, s - b = 1.5 - 1 = 0.5 and s - c = 1.5 - 1 = 0.5$ $implies s-a=1.5-1=2, s-b=1.5-1=0.5 and s-c=1.5-1=0.5$
$\Rightarrow s - a = 0.5, s - b = 0.5 and s - c = 0.5$ $implies s-a=0.5, s-b=0.5 and s-c=0.5$

$\Rightarrow A r e a = \sqrt{1.5 \cdot 0.5 \cdot 0.5 \cdot 0.5} = \sqrt{0.1875} = 0.433$ $implies Area=sqrt(1.5*0.5*0.5*0.5)=sqrt0.1875=0.433$ square units

$\Rightarrow A r e a = 0.433$ $implies Area=0.433$ square units

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