How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 15, and 9 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 7, 15, and 9 units in length?

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Answer 1 · 2016-02-13T12:23:25

Area $\approx 43.39$ $~~43.39$ sq. units.

Explanation:

Heron's formula tells us that the area of a triangle with sides $a, b, and c$ $a, b, and c$ is
$XXX {Area}_{△} = \sqrt{s (s - a) (s - b) (s - c)}$ $color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))$
where $s$ $s$ is the semi-perimter ( $\frac{a + b + c}{2}$ $(a+b+c)/2$ ).

In this case we have
$XXX a = 7 XX b = 15 XX c = 9 and XX s = \frac{31}{2}$ $color(white)("XXX")a=7 color(white)("XX")b=15 color(white)("XX")c=9 and color(white)("XX")s=31/2$

So
$A r e a_{△} = \sqrt{\frac{31}{2} \times \frac{17}{2} \times \frac{1}{2} \times \frac{13}{2}}$ $Area"_triangle = sqrt(31/2xx17/2xx1/2xx13/2)$

$XXXX \approx 41.39$ $color(white)("XXXX")~~41.39$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 15, and 9 units in length?

1 Answer

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