How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 13 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 15, 16, and 13 units in length?

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Answer 1 · 2018-05-02T08:26:19

$area \approx 91.192 to 3 dec. places$ $"area "~~91.192" to 3 dec. places"$

Explanation:

$the area (A) of a triangle using Heron's formula$ $"the area (A) of a triangle using "color(blue)"Heron's formula"$ is.

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

$where s is the semi-perimeter and a, b, c the sides of$ $"where s is the semi-perimeter and a, b, c the sides of "$
$the triangle$ $"the triangle"$

$let a = 15, b = 16 and c = 13$ $"let "a=15,b=16" and "c=13$

$\Rightarrow s = \frac{15 + 16 + 13}{2} = \frac{44}{2} = 22$ $rArrs=(15+16+13)/2=44/2=22$

$\Rightarrow A = \sqrt{22 (22 - 15) (22 - 16) (22 - 13)}$ $rArrA=sqrt(22(22-15)(22-16)(22-13))$

$\Rightarrow A = \sqrt{22 \times 7 \times 6 \times 9}$ $color(white)(rArrA)=sqrt(22xx7xx6xx9)$

$\Rightarrow A = \sqrt{8316} \approx 91.192$ $color(white)(rArrA)=sqrt8316~~91.192$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 13 units in length?

1 Answer

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