Question

14. The side of a triangle
are 12cm, 35cm and 37 cm
Find its area
​

Answer 1

The sides of the triangle are 12 cm, 35 cm and 37 cm.

Using Heron's formula therefore,

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$:\implies\tt s = \dfrac{a + b + c}{2} \\\\\\:\implies\tt s = \dfrac{12 + 35 + 37}{2} \\\\\\:\implies\tt s = \cancel\dfrac{84}{2}\\\\\\:\implies{\underline{\boxed{\tt{s = 42\; cm}}}}$

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$\therefore{\underline{\sf{Hence, \; Semiperimeter\;of\;the\;\triangle\;is\;\bf{ 42\;cm}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\bf{\dag} \:\boxed{\sf{\pink{Area_{\triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}}$

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$:\implies\tt Area_{\triangle} = \sqrt{s(s - a) (s - b) (s - c)} \\\\\\:\implies\tt Area_{\triangle} = \sqrt{42(42 - 12) (42 - 35) (42 - 37)} \\\\\\:\implies\tt Area_{\triangle} = \sqrt{42 \times 30 \times 7 \times 5}\\\\\\:\implies\tt Area_{\triangle} = \sqrt{2 \times 3 \times 7 \times 7 \times 5 \times 2 \times 3 \times 5}\\\\\\:\implies\tt Area_{\triangle} = 2 \times 3 \times 5 \times 7\\\\\\:\implies{\underline{\boxed{\tt{Area_{\triangle} = 210\;cm^2}}}}$

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$\therefore{\underline{\sf{Hence,\;area\;of\;the\:\triangle\;is\; \bf{210\;cm^2 }.}}}$

Answer 2

Given :-

• First Side of Triangle = 12cm
• Second Side of Triangle = 35cm
• Third Side of Triangle = 37cm

To Find :-

• Area of the Triangle

Solution :-

Using Heron's Formula :

⇒ S = A + B + C / 2

⇒ S = 12 + 35 + 37 / 2

⇒ S = 47 + 37 / 2

⇒ S = 84 / 2

⇒ S = 42cm

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Area of Triangle :

⇒ Area of Triangle = √S ( S-a ) ( S-b ) ( S-c )

⇒ Area = √42 (42 - 12) (42 - 35) (42 - 37)

⇒ Area = √42 ( 30 ) ( 7 ) ( 5 )

⇒ Area = √42 × 30 × 7 × 5

⇒ Area = √1260 × 35

⇒ Area = √44100

⇒ Area = 210cm²

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Therefore, The area of triangle is 210cm²

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