How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ $4$ , $8$ $8$ , and $5$ $5$ ?

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How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ $4$ , $8$ $8$ , and $5$ $5$ ?

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Answer 1 · 2016-02-12T07:40:06

$A = 8.1815$ $A=8.1815$

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, $a, b, and c$ $a, b, and c$ are the sides, and $s$ $s$ is the semiperimeter, which is the perimeter divided by $2$ $2$ . Side $a = 4$ $a=4$ , side $b = 8$ $b=8$ , and side $c = 5$ $c=5$ .

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

$s = \frac{4 + 8 + 5}{2}$ $s=(4+8+5)/2$

$s = \frac{17}{2}$ $s=17/2$

$s = 8.5$ $s=8.5$

Use Heron's formula to find the area of the triangle.

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

Substitute the known values into the equation.

$A = \sqrt{(8.5) (8.5 - 4) (8.5 - 8) (8.5 - 5)}$ $A=sqrt((8.5)(8.5-4)(8.5-8)(8.5-5)$

Simplify.

$A = \sqrt{(8.5) (4.5) (0.5) (3.5)}$ $A=sqrt((8.5)(4.5)(0.5)(3.5)$

Simplify.

$A = \sqrt{66.9375}$ $A=sqrt(66.9375)$

Take the square root.

$A = 8.1815$ $A=8.1815$ square units to four decimal places.

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How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ $4$ , $8$ $8$ , and $5$ $5$ ?

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How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ $4$ , $8$ $8$ , and $5$ $5$ ?