How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 7, and 10 units in length?

Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 7, and 10 units in length?

1 Answer

Impact of this question

1994 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-07T07:46:04

$A = \frac{\sqrt{210}}{2} s q . c m$ $A=(sqrt(210))/2 sq.cm$

Explanation:

Heron's formula

$s = \frac{a + b + c}{2}$ $s=(a+b+c)/2$

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

In your question
triangle with side lengths of 12,7,10

$s = \frac{12 + 7 + 10}{2}$ $s=(12+7+10)/2$
$s = \frac{19}{2}$ $s=19/2$

$A = \sqrt{\frac{19}{2} (\frac{19}{2} - 7) (\frac{19}{2} - 12) (\frac{19}{2} - 10)}$ $A=sqrt(19/2(19/2-7)(19/2-12)(19/2-10))$
$A = \sqrt{\frac{12}{2} (\frac{14}{2}) (- \frac{5}{2}) (- \frac{1}{2})}$ $A=sqrt(12/2(14/2)(-5/2)(-1/2))$
$A = \sqrt{\frac{840}{16}}$ $A=sqrt(840/16)$
$A = \frac{2 \sqrt{210}}{4}$ $A= (2sqrt(210))/4$
$A = \frac{\sqrt{210}}{2} s q . c m$ $A=(sqrt(210))/2 sq.cm$

Science

Math

Humanities

... and beyond

How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 7, and 10 units in length?

1 Answer

Explanation:

Related questions

Impact of this question