Question

find the area of a triangle whose side are 10 centimeter ,12cm,14cm. ​

Answer 1

$\bf{\underline{\underline{Answer:}}}$

$\bf{\therefore Area \:of \:Triangle = 24 \sqrt{6}\:cm^2 \:or \:58.78\: cm^2}$

$\bf{\underline {Given:}}$

• ABC is a triangle.
• Side a = 10 cm
• Side b = 12 cm
• Side c = 14 cm

$\bf{\underline {To\:Find:}}$

• The semi perimeter (s) of triangle

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Semi perimeter of triangle,

$s = \dfrac{(a+b+c)}{2}\: unit\\ \\</p><p>=\dfrac{(10+12+14)}{2} cm\\ \\</p><p>=\dfrac{36}{2}cm \\ \\= 18 cm$

Finding the area of triangle by using the heron's formula :-

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

Area of triangle

$\begin{lgathered}= \sqrt{18(18 - 10)(18 - 12)(18 - 14)} \\ \\ = \sqrt{18 \times 8 \times 6 \times 4} \\ \\ = \sqrt{2 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2} \\ \\ = 2 \times 2 \times 2 \times 3 \times \sqrt{2 \times 3 } \\ \\ = 24 \sqrt{6}\end{lgathered}$

$\bf{\therefore Area \:of \:Triangle = 24 \sqrt{6}\:cm^2 \:or \:58.78\: cm^2}$

Answer 2

Question:

Find the area of a triangle whose side are 10 cm, 12cm, 14cm.

Solution :

$\underline{\bold{Given:}}$

• Sides of the triangle = 10 cm, 12 cm and 14 cm.

$\underline{\bold{To\:Find:}}$

• Area of the triangle.

Let

• A=10 cm
• B=12 cm
• C=14 cm

$\boxed {\purple{S=(\frac{A + B + C}{2})\:unit}}$

$\implies S=(\frac{A + B + C}{2} )\:unit\\ \implies S = (\frac{10 + 12 + 14}{2} ) \:cm \\ \implies S= \frac{36}{2} \: cm \\ \implies S=18 \: cm$

$\boxed{\purple{Area= \sqrt{s(s - a)(s - b)(s - c)}\:sq.units}}$

$\implies Area= \sqrt{s(s - a)(s - b)(s - c)} \: sq.units\\ \implies Area= \sqrt{18(18 - 10)(18 - 12)(18 - 14)} \:cm^2\\ \implies Area= \sqrt{18 \times 8 \times 6 \times 4} \:cm^2 \\ \implies Area= \sqrt{2 \times 3 \times 3 \times 2 \times 2 \times 2 \times2 \times 3 \times 2 \times 2} \:cm^2 \\ \implies Area= 2 \times 2 \times 2 \times 3 \sqrt{2 \times3 } \:cm^2 \\ \implies Area = 24 \sqrt{6}\:cm^2$

$\boxed {\green{\therefore {Area\:of\:the\:triangle\:is \:24 \sqrt{6}\:cm^2.}}}$