Question

The side of a traingle are 3cm,3cm and 5 cm . Find its area​

Answer 1

Given :

• 1st side of Triangle = 3 cm
• 2nd side of triangle = 3 cm
• 3rd side of triangle = 5 cm

To Find :

• Area = ?

SolutioN :

$\dag$ Calculating the Semi - Perimeter :

$\bigstar$ As we know the formula for Semi - Perimeter :

$\large{\star{\pmb{\underline{\boxed{\pmb{\sf{ Semi - Perimeter = \dfrac{ S_1 + S_2 + S_3}{2} }}}}}}}\star$

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$\bigstar$ Putting the Values :

${\implies{\qquad{\sf{ Semi - Perimeter = \dfrac{S_1 + S_2 + S_3}{2} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Semi - Perimeter = \dfrac{3 + 3 + 5}{2} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Semi - Perimeter = \dfrac{11}{2} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Semi - Perimeter = \cancel\dfrac{11}{2} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\purple{\pmb{\sf{ Semi - Perimeter = 5.5 \; cm }}}}}}}}$

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$\dag$ Calculating the Area :

$\bigstar$ As we know the formula for Area :

$\large{\star{\pmb{\underline{\boxed{\pmb{\sf{ Area = \sqrt{s (s - a)(s - b)(s - c)} }}}}}}}\star$

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$\bigstar$ Putting th Values :

${\dashrightarrow{\qquad{\sf{ Area = \sqrt{s (s - a)(s - b)(s - c)} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \sqrt{5.5 (5.5 - 3)(5.5 - 3)(5.5 - 5)} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \sqrt{5.5 \times 2.5 \times 2.5 \times 0.5} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \sqrt{0.5 \times 11 \times 0.5 \times 5 \times 0.5 \times 5 \times 0.5} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = 0.5 \times 0.5 \times 5 \times \sqrt{11} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = 0.5 \times 2.5 \times \sqrt{11} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = 1.25 \times \sqrt{11} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\red{\pmb{\sf{ Area = 1.25 \sqrt{11} \; {cm}^{2} }}}}}}}}$

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$\dag$ Therefore :

❛❛ Area of the given Triangle is 1.25√11 cm² . ❜❜

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