Question

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

Answer 1

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

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

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

$\dashrightarrow\sf s = \dfrac{a + b + c}{2}\\\\\\\dashrightarrow\sf s = \dfrac{14 + 15 + 11}{2}\\\\\\\dashrightarrow\sf s = \cancel\dfrac{40}{2}\\\\\\\dashrightarrow\underline{\boxed{\pmb{\frak{s = 20\;cm}}}}$

$\therefore$ Semi perimeter of the given triangle is 20 cm.

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$\bigstar\:{\underline{\bf{Using\:Heron's\:formula\:to\:find\:Area\:of\:\triangle\::}}}$

$\bigstar\:{\underline{\boxed{\pmb{\sf{Area_{\: (triangle)} = \sqrt{s\bigg(s - a\bigg)\bigg(s - b\bigg)\bigg(s - c\bigg)}}}}}}$

$\dashrightarrow\sf Area_{\;(triangle)} = \sqrt{20\Big(20 - 14\Big)\Big(20 - 15\Big)\Big(20 - 11\Big)}\\\\\\\dashrightarrow\sf Area_{\;(triangle)} = \sqrt{20 \times 6 \times 5 \times 9}\\\\\\\dashrightarrow\sf Area_{\;(triangle)} =\sqrt{5400}\\\\\\\dashrightarrow{\underline{\boxed{\pmb{\frak{\pink{73.48\:cm^2}}}}}}\:\bigstar\\\\\\ \therefore\:{\underline{\sf{Area\:of\:the\;triangle\:is\:{\sf{\pmb{73.48\:cm^2}}}}}}.$

Answer 2

Answer:

Given :-

• If the sides of a triangle are 14 cm,15cm,11 cm.

□To prove :-

• Find the area of triangle.

□Solution :-

• Here we know that to first finding the semi perimeter to this.

$semi \: perimeter = \frac{a + b + c}{2}$

• Now applying the values we get that,

• $semi \: perimeter = \frac{14 + 15 + 11}{2}$
• $semi \: perimeter = \frac{40}{2} = 20cm$
• Here by using Heron's formula we get area of triangle answer to your question.

• $area of triangle = \sqrt{s(s - a)(s - b)(s - c} )$

• Here ,

• a=14cm
• b=15cm
• c=11cm.

• Now applying the values we get that,

• $area of triangle = \sqrt{20(20 - 14)(20 - 15)(20 - 11} )$
• $area of triangle = \sqrt{20 \times 6 \times 5 \times 9}$
• $area = \sqrt{5400} = 73.48cm^2$

□Hence,

• The area of triangle =73.48cm^2