A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

Question

A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

1 Answer

Impact of this question

1804 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-07T06:15:45

The area of the triangle is 53.5 square units.

Explanation:

Heron's formula is $A = \sqrt{s (s - a) (s - b) (s - c)}$ $A=sqrt(s(s-a)(s-b)(s-c))$ , where $A$ $A$ is area, $a, b,$ $a, b,$ and $c$ $c$ are the sides of the triangle, and $s$ $s$ is the semiperimeter, which is half the perimeter.

The formula for the semiperimeter is $s = \frac{a + b + c}{2}$ $s=(a+b+c)/2$ .

Let side $a = 14$ $a=14$ , side $b = 9$ $b=9$ , and side $c = 12$ $c=12$ .

Calculate the semiperimeter.

$s = \frac{14 + 9 + 12}{2}$ $s=(14+9+12)/2$

$s = \frac{35}{2} = 17.5$ $s=35/2=17.5$

Calculate the area of the triangle.

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

$A = \sqrt{(17.5) (17.5 - 14) (17.5 - 9) (17.5 - 12)}$ $A=sqrt((17.5)(17.5-14)(17.5-9)(17.5-12))$

$A = 53.5$ $A=53.5$ square units

Source: https://www.mathsisfun.com/geometry/herons-formula.html

Science

Math

Humanities

... and beyond

A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

1 Answer

Explanation:

Related questions

Impact of this question