Find the area of triangle abc if a=11, b=9, c=5?

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Find the area of triangle abc if a=11, b=9, c=5?

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Answer 1 · 2018-03-07T14:34:09

$22.19$ $22.19$

Explanation:

We know that area of $△ A B C = △ = \sqrt{s (s - a) (s - b) (s - c)}$ $triangleABC=triangle=color(red)(sqrt(s(s-a)(s-b)(s-c))$
where, $2 s = a + b + c$ $2s=a+b+c$ .
Taking, $a = 11, b = 9, c = 5$ $a=11,b=9,c=5$ ,we have, $2 s = 11 + 9 + 5 = 25 \Rightarrow s = 12.5$ $2s=11+9+5=25rArrs=12.5$
$△ = \sqrt{12.5 (12.5 - 11) (12.5 - 9) (12.5 - 5)}$ $triangle=sqrt(12.5(12.5-11)(12.5-9)(12.5-5))$
$= \sqrt{(12.5) (1.5) (3.5) (7.5)} \approx 22.19$ $=sqrt((12.5)(1.5)(3.5)(7.5))~~22.19$

Answer 2 · 2018-03-07T14:38:16

$22.16 {cm}^{2}$ $22.16 " cm"^2$

Explanation:

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

According to Heron's formula ,

Area of triangle $= \sqrt{S (S - a) (S - b) (S - c)}$ $= sqrt[S(S-a)(S-b)(S-c)]$

Here , $S = Semiperimeter of △ a b c$ $S = "Semiperimeter of" triangleabc$

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

$\Rightarrow \frac{11 + 9 + 5}{2}$ $=> (11+9+5)/2$

$\Rightarrow \frac{25}{2} cm$ $=> 25/2 "cm"$

And $a = 11 cm$ $a=11" cm"$

$b = 9 cm$ $b=9" cm"$

$c = 5 cm$ $c=5" cm"$

Put these values in the herons formula.

$\Rightarrow \sqrt{\frac{25}{2} (\frac{25}{2} - 11) (\frac{25}{2} - 9) (\frac{25}{2} - 5)}$ $=> sqrt[25/2(25/2-11)(25/2-9)(25/2-5)]$

$\Rightarrow \sqrt{\frac{25}{2} \times \frac{3}{2} \times \frac{7}{2} \times \frac{15}{2}}$ $=> sqrt[25/2xx3/2xx7/2xx15/2$

$\Rightarrow \sqrt{\frac{5}{2} \times \frac{5}{2} \times \frac{3}{2} \times \frac{3}{2} \times 5 \times 7}$ $=> sqrt(5/2xx5/2xx3/2xx3/2xx5xx7$

$\Rightarrow \frac{5}{2} \times \frac{3}{2} \times \sqrt{5 \times 7}$ $=> 5/2xx3/2xxsqrt(5xx7$

$\Rightarrow \frac{15}{4} \times \sqrt{35}$ $=> 15/4xxsqrt35$

$\Rightarrow 3.75 \sqrt{35}$ $=> 3.75sqrt35$

$\Rightarrow 3.75 \times 5.91$ $=> 3.75xx5.91$

$\Rightarrow 22.1625 {cm}^{2}$ $=> 22.1625" cm"^2$

$\Rightarrow 22.16 {cm}^{2} approximately$ $=> 22.16 " cm"^2 "approximately"$

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Find the area of triangle abc if a=11, b=9, c=5?

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