A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

Question

A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

1 Answer

Impact of this question

1928 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-05T00:37:52

$A = 2 \sqrt{182}$ $A=2sqrt182$

Explanation:

First, find the triangle's semiperimeter. The semiperimeter is one half the perimeter of the triangle, which can be represented for a triangle with sides $a, b,$ $a,b,$ and $c$ $c$ as

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

Thus,

$s = \frac{6 + 11 + 9}{2} = 13$ $s=(6+11+9)/2=13$

Now, use Heron's formula to determine the area of the triangle. Heron's formula uses only the side lengths of the triangle to find the triangle's area:

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

$A = \sqrt{13 (13 - 6) (13 - 11) (13 - 9)}$ $A=sqrt(13(13-6)(13-11)(13-9))$

$A = \sqrt{13 \times 7 \times 2 \times 4}$ $A=sqrt(13xx7xx2xx4)$

$A = 2 \sqrt{182}$ $A=2sqrt182$

Science

Math

Humanities

... and beyond

A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

1 Answer

Explanation:

Related questions

Impact of this question