Question

using heron's formula find the area of a triangle whose sides are 20 cm 30 cm 40 cm​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• 1st side of triangle = 20 cm

• 2nd side of triangle = 30 cm

• 3rd side of triangle = 40 cm

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Area of triangle using heron's formula

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{Heron's formula :}}}$

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➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$

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Where ,

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• s = Semi perimeter

• a = 1st side

• b = 2nd side

• c = 3rd side

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ՏᗴᗰI ᑭᗴᖇIᗰᗴTᗴᖇ

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➠ $\sf \dfrac { Perimeter } { 2 }$

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Perimeter of triangle

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Side 1 + Side 2 + Side 3

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➜ 20 + 30 + 40

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➨ 90

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Semi perimeter

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➜ $\sf \dfrac { 90 } { 2 }$

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➨ 45

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$\underline{\bold{\texttt{Heron's formula formula in given triangle :}}}$

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➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$ ----- (1)

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Where ,

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• s = 45

• a = 20

• b = 30

• c = 40

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⟮ Putting these values in (1) ⟯

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➜ $\sf \sqrt { 45(45 - 20)(45 - 30)(45 - 40) }$

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➜ $\sf \sqrt { 45(25)(15)(5) }$

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➜ $\sf \sqrt { 225 \times 25 \times 15 }$

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➜ $\sf 15 × 5 \sqrt { 15 }$

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➜ 75 × 3.87

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➨ 290.25 sq. cm

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• Hence the area of triangle is 290.25 sq. cm.

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Answer 2

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

$\underline{\bold{\texttt{Heron's formula :}}}$

$\:\:$

➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$

$\:\:$

Where ,

$\:\:$

s = Semi perimeter

a = 1st side

b = 2nd side

c = 3rd side

$\:\:$

ՏᗴᗰI ᑭᗴᖇIᗰᗴTᗴᖇ

$\:\:$

➠ $\sf \dfrac { Perimeter } { 2 }$

$\:\:$

Perimeter of triangle

$\:\:$

Side 1 + Side 2 + Side 3

$\:\:$

➜ 20 + 30 + 40

$\:\:$

➨ 90

$\:\:$

Semi perimeter

$\:\:$

➜ $\sf \dfrac { 90 } { 2 }$

$\:\:$

➨ 45

$\:\:$

$\underline{\bold{\texttt{Heron's formula formula in given triangle :}}}$

$\:\:$

➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$ ----- (1)

$\:\:$

Where ,

$\:\:$

s = 45

a = 20

b = 30

c = 40

$\:\:$

⟮ Putting these values in (1) ⟯

$\:\:$

➜ $\sf \sqrt { 45(45 - 20)(45 - 30)(45 - 40) }$

$\:\:$

➜ $\sf \sqrt { 45(25)(15)(5) }$

$\:\:$

➜ $\sf \sqrt { 225 \times 25 \times 15 }$

$\:\:$

➜ $\sf 15 × 5 \sqrt { 15 }$

$\:\:$

➜ 75 × 3.87

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➨ 290.25 sq. cm

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Hence the area of triangle is 290.25 sq. cm.

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