Question

if the sides of a triangular field are 290 m290 and 400 metre by the area of the field​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sides of triangle = 290m , 290m , 400m

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Area = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Semi\: Perimeter = \dfrac{perimeter}{2}}}}}$

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$\sf: \implies{\bold{ Semi\: Perimeter = \dfrac{290 + 290 + 400}{2}}}$

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$\sf: \implies{\bold{ Semi\: Perimeter = \dfrac{ 980 }{2}}}$

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$\sf: \implies{\bold{Semi\: perimeter = 490}}$

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$\sf{\red{\boxed{\bold{area =\sqrt{ s ( s - a )( s - b)( s - c )}}}}}$

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$\sf: \implies{\bold{area =\sqrt{ 490( 490 - 290)( 490 - 290)( 490 - 400)}}}$

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$\sf: \implies{\bold{area =\sqrt{ 490 \times 200 \times 200 \times 90}}}$

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$\sf: \implies{\bold{area =\sqrt{ 7\times 7\times 10\times 10 \times 10 \times 2 \times 2 \times 10 \times 10 \times 3 \times 3\times 10}}}$

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$\sf: \implies{\bold{ area = 7 \times 2\times 3\times 10 \times 10 \times \times 10 }}$

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$\sf: \implies{\bold{area = 42 \times 1000}}$

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$\sf: \implies{\bold{area = 42000 cm^2}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Area of Triangular field is 42000cm^2

Answer 2

Given:

• Sides of triangle are 290m, 290m and 400m

Find:

• Area of the Triangle

Solution:

we, know that

⎆$\sf s = \dfrac{sum \: of \: all \: sides \: of \: triangle}{2}$

So,

$\overline{\underbrace{\boxed{\sf s = \dfrac{a + b + c}{2}}}}$

Now,

$\sf\to s = \dfrac{a + b + c}{2}$

$\sf\to s = \dfrac{290 + 290+ 400}{2}$

$\sf\to s = \cancel{\dfrac{980}{2}} = 490m$

$\sf\to s = 490m$

So, s = 490m

Now,

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

So,

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

$\sf \Rrightarrow Area \: of \: triangle = \sqrt{490(490 - 290)(490 - 290)(490 - 400)}$

$\sf \Rrightarrow Area \: of \: triangle = \sqrt{490(200)(200)(90)}$

$\sf \Rrightarrow Area \: of \: triangle = \sqrt{490 \times 3600000}$

$\sf \Rrightarrow Area \: of \: triangle = \sqrt{1764000000}$

$\sf \Rrightarrow Area \: of \: triangle = 42000m$

Hence, area of triangular plot is 42000m