How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 3, and 7 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 9, 3, and 7 units in length?

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Answer 1 · 2016-01-22T18:38:01

$A r e a = 8.7856$ $Area=8.7856$ square units

Explanation:

Hero'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 $a = 9, b = 3$ $a=9, b=3$ and $c = 7$ $c=7$

$\Rightarrow s = \frac{9 + 3 + 7}{2} = \frac{19}{2} = 9.5$ $implies s=(9+3+7)/2=19/2=9.5$

$\Rightarrow s = 9.5$ $implies s=9.5$

$\Rightarrow s - a = 9.5 - 9 = 0.5, s - b = 9.5 - 3 = 6.5 and s - c = 9.5 - 7 = 2.5$ $implies s-a=9.5-9=0.5, s-b=9.5-3=6.5 and s-c=9.5-7=2.5$
$\Rightarrow s - a = 0.5, s - b = 6.5 and s - c = 2.5$ $implies s-a=0.5, s-b=6.5 and s-c=2.5$

$\Rightarrow A r e a = \sqrt{9.5 \cdot 0.5 \cdot 6.5 \cdot 2.5} = \sqrt{77.1875} = 8.7856$ $implies Area=sqrt(9.5*0.5*6.5*2.5)=sqrt77.1875=8.7856$ square units

$\Rightarrow A r e a = 8.7856$ $implies Area=8.7856$ square units

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How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 3, and 7 units in length?

1 Answer

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