Question

If the sides of a triangle are 26 cm, 28 cm and 30 cm. Find the area of triangle.

For Class 9​

Answer 1

Given :

• Side 1 of Triangle = 26 cm
• Side 2 of Triangle = 28 cm
• Side 3 of Triangle = 30 cm

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To Find :

• Area of the Triangle = ?

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Solution :

$\blue{❒}$ Formula Used :

$\large{\pink{\bigstar \: \: {\underbrace{\underline{\purple{\sf{ Area{\small_{(Triangle)}} = \sqrt{s (s - a )(s - b)(s - c)} }}}}}}}$

Where :

• ➳ S = Semi - Perimeter
• ➳ a = Side 1
• ➳ b = Side 2
• ➳ c = Side 3

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$\blue{❒}$ Calculating the Area :

• Semi - Perimeter :

${\longmapsto{\qquad{\sf{ S = \dfrac{a + b + c}{2}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ S = \dfrac{ 26 + 28 + 30}{2}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ S = \cancel\dfrac{84}{2}}}}} \\ \\ \ {\qquad{\textsf{ Semi - Perimeter of Triangle = {\blue{\sf{ 42 \: cm }}}}}}$

• Area :

${\longmapsto{\qquad{\sf{ Area = \sqrt{s (s - a )(s - b)(s - c)} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \sqrt{42 (42 - 26)(42 - 28)(42 - 30)} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \sqrt{42 \times 16 \times 14 \times 12} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \sqrt{ 7 \times 6 \times 16 \times 7 \times 2 \times 6 \times 2} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \sqrt{ 7 \times 6 \times 2 \times \sqrt{16}} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \sqrt{ 84 \times \sqrt{16}}}}}} \: \: \: \: {\bigg\lgroup{\green{\sf{ Taking \: \sqrt{16} \: = \: 4 }}}\bigg\rgroup} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = 84 \times 4 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Triangle = {\red{\sf{ 336 \: cm² }}}}}}$

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$\blue{❒}$ Therefore :

❝ Area of the given Triangle is 336 cm² . ❞

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Answer 2

Step-by-step explanation:

Given

• If the sides of a triangle are 26 cm, 28 cm and 30 cm. Find the area of triangle.

To Find

• Area Of Triangle

Solution

${ \qquad {\underline {\underline {\sf{ \bold{Let}}}}}}$

The sides of triangle be

• a = 26 cm
• b = 28 cm
• c = 30 cm
• Let S be the semi-perimeter of the triangle.

We Know,

$\green \bigstar { \underline {\boxed{ \sf{S= \: \frac{ \red{a} \green{+ b} \pink{ + c}} \purple{2} }}}}$

~Putting Terms According It

$\qquad \sf \longmapsto \pink{ \frac{26 + 28 + 30}{2} }$

$\qquad \sf \longmapsto { \frac{26 + 28 + 30}{2} = \red{\frac{84}{2} } =42cm }$

By Heron's Formula

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

So,

$\sf{\longmapsto \: Area \small_{ (\triangle)} = \sqrt{42 \times 42 - 26(42 - 28)(42 - 30 )} }$

$\sf{\longmapsto \: Area \small_{ (\triangle)} = \sqrt{42 \times 16 \times 14 \times 12 )} }$

$\sf{\longmapsto \: Area \small_{ (\triangle)} = \sqrt{7 \times 6 \times 16 \times 7 \times 2 \times 6 \times 2)} = 336cm {}^{2} }$

${\boxed {\boxed{ \sf \underline \pink{336 {}^{2}cm }}}}$

Therefore,

$\sf{Area \small_{ (\triangle )} = {\boxed {\boxed{ \sf \underline \pink{336 {}^{2}cm }}}} }$