Question

7) If the sides of a triangle are 14 cm, 15 cm and 11 cm, then the area of the triangle is

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Answer 1

Answer:

The area of the triangle 2310squarecm or you can say 23.1squaremetre

Step-by-step explanation:

The sides of the triangle are 14cm , 15cm and 11cm.

The area is 14 x 15 x 11= 2310squarecm.

The area of the triangle 2310squarecm or you can say 23.1squaremetre

Answer 2

Given: 

• The sides of a triangle are 14cm, 15cm and 11cm respectively.

To find:

• Area of triangle

Solution:

Let's Consider the given triangle of a, b and c be 14cm, 15cm and 11cm.⠀⠀

» As we know that semi perimeter of the triangle is sum of all sides i.e (s) = (a + b + c)/2. 

Therefore,

$\begin{gathered} : \implies\sf s = \dfrac{a + b + c}{2}\\\\\\ : \implies \sf s = \dfrac{14 + 15 + 11}{2}\\\\\\ : \implies\sf s = \cancel\dfrac{40}{2}\\\\\\ : \implies\underline{\boxed{{\frak{s = 20\;cm}}}} \color{navy} \bigstar\\\\\end{gathered}$

∴ Semi perimeter of the given triangle is 20 cm.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

$\begin{gathered} \red\bigstar {\underline{\sf{Using\:Heron's\:formula\:to\:find\:Area\:of\:\triangle\::}}}\\\\\end{gathered}$

$\begin{gathered} \orange\bigstar{\underline{\boxed{{\frak {Area_{\: (triangle)} = \sqrt{s\bigg(s - a\bigg)\bigg(s - b\bigg)\bigg(s - c\bigg)}}}}}}\\\\\end{gathered}$

$\begin{gathered}: \implies\sf Area_{\;(triangle)} = \sqrt{20\Big(20 - 14\Big)\Big(20 - 15\Big)\Big(20 - 11\Big)}\\ \\ \\\\ : \implies\sf Area_{\;(triangle)} = \sqrt{20 \times 6 \times 5 \times 9}\\ \\ \\ \\: \implies\sf Area_{\;(triangle)} =\sqrt{5400}\\ \\ \\\\ : \implies{\underline{\boxed{{\frak{{73.48\:cm^2}}}}}}\pink\bigstar \\ \\ \end{gathered}$

$\begin{gathered} \therefore\:{\underline{\sf{Area\:of\:the\;triangle\:is\:{\sf{\pmb{73.48\:cm^2}}}}}}.\end{gathered}$

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