Find the area of a triangle.its two sides are 18cm and 10cm, perimeter

1.	Find the area of a triangle.its two sides are 18cm and 10cm, perimeter is 42 cm
Answer» ALIGN="absmiddle" ALT="\sf \bf \huge {\boxed {\MATHBB {QUESTION}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%5Csf%20%5Cbf%20%5Chuge%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BQUESTION%7D%7D%7D%20" title="\sf \bf \huge {\boxed {\mathbb {QUESTION}}}"> $\tt Find \:the\: area\: of \:a \:triangle.\:Its\: two \:sides \:are\: 18\:cm\\\tt and\: 10\:cm, \:perimeter\: is\: 42\: cm.$ $\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$ $\sf \bf {\boxed {\mathbb {GIVEN}}}$ $\bf First \:side\:of\:the \:triangle(a) = 18\:cm$ $\bf Second\:side\:of\:the \:triangle(b) = 10\:cm$ $\bf Perimeter \:the \:triangle(P) = 42\:cm$ $\sf \bf {\boxed {\mathbb {TO\:FIND}}}$ $\bf Area\:of\:the \:triangle(A)$ $\sf \bf {\boxed {\mathbb {SOLUTION}}}$ ${\pink {\underline {\bf {\pmb {Third \:side\:of\:the \:triangle(c)}}}}}$ ${\blue {\boxed {\boxed {\boxed {\green {\pmb {P_{(Triangle)}=a+b+c}}}}}}}$ $\sf P= perimeter\:of\:the \:triangle$ $\sf a=first \:side \:of\:the \:triangle$ $\sf b=second\:side \:of\:the \:triangle$ $\sf c=third \:side \:of\:the \:triangle$ ${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$ $\bf \implies 42=18+10+c$ $\bf \implies 42=28+c$ $\bf \implies c=42-28$ $\implies {\blue {\boxed {\boxed {\purple {\sf c=14\:cm}}}}}$ —————————————————————————————— ${\pink {\underline {\bf {\pmb {Semiperimeter \:of\:the \:triangle(S)}}}}}$ ${\blue {\boxed {\boxed {\boxed {\green {\pmb {S=\dfrac{P}{2}}}}}}}}$ $\sf S=semiperimeter \:of\:the \:triangle$ $\sf P=perimeter \:of\:the \:triangle$ ${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$ $\bf \implies S=\dfrac{42}{2}$ $\bf \implies S=\dfrac{\cancel{42}}{\cancel{2}}$ $\implies {\blue {\boxed {\boxed {\purple {\sf S=21\:cm}}}}}$ *——————————————————————————————* ${\pink {\underline {\bf {\pmb {Area \:of\:the \:triangle(A)}}}}}$ ${\blue {\boxed {\boxed {\boxed {\green {\pmb {A_{(Triangle)}=\sqrt{S\Big(S-a\Big) \Big(S-b\Big) \Big(S-c\Big)}}}}}}}}$ $\sf A=area\:of \:the \:triangle$ $\sf S=semiperimeter \:of\:the \:triangle$ $\sf a=first \:side \:of\:the \:triangle$ $\sf b=second\:side \:of\:the \:triangle$ $\sf c=third \:side \:of\:the \:triangle$ ${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$ $\bf \implies A=\sqrt{21\Big(21-18\Big) \Big(21-10\Big) \Big(21-14\Big)}$ $\bf \implies A=\sqrt{21\Big(3\Big) \Big(11\Big) \Big(7\Big)}$ $\bf \implies A=\sqrt{21\times 3\times 11\times 7}$ $\bf \implies A=\sqrt{4851}$ $\bf \implies A=\sqrt{441\times 11}$ ${\blue {\boxed {\boxed {\purple {\mathfrak {A=21\sqrt{11}\:{cm}^{2}}}}}}}$ ${\underbrace {\red {\overline {\red {\underline {\red {\pmb {\sf {{\therefore} The\:area \:of \:the \:triangle \:is\:21\sqrt{11}\:{cm}^{2}}}}}}}}}}$ $\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$ ____________________________________________ $\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$ $\sf Area \:of \:the \:triangle = \dfrac{1}{2}bh$ $\sf Perimeter\:of \:the \:triangle =a+b+c$

Find the area of a triangle.its two sides are 18cm and 10cm, perimeter is 42 cm

Answer» ALIGN="absmiddle" ALT="\sf \bf \huge {\boxed {\MATHBB {QUESTION}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%5Csf%20%5Cbf%20%5Chuge%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BQUESTION%7D%7D%7D%20" title="\sf \bf \huge {\boxed {\mathbb {QUESTION}}}">

$\tt Find \:the\: area\: of \:a \:triangle.\:Its\: two \:sides \:are\: 18\:cm\\\tt and\: 10\:cm, \:perimeter\: is\: 42\: cm.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

$\bf First \:side\:of\:the \:triangle(a) = 18\:cm$
$\bf Second\:side\:of\:the \:triangle(b) = 10\:cm$
$\bf Perimeter \:the \:triangle(P) = 42\:cm$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

$\bf Area\:of\:the \:triangle(A)$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Third \:side\:of\:the \:triangle(c)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {P_{(Triangle)}=a+b+c}}}}}}}$

$\sf P= perimeter\:of\:the \:triangle$
$\sf a=first \:side \:of\:the \:triangle$
$\sf b=second\:side \:of\:the \:triangle$
$\sf c=third \:side \:of\:the \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 42=18+10+c$

$\bf \implies 42=28+c$

$\bf \implies c=42-28$

$\implies {\blue {\boxed {\boxed {\purple {\sf c=14\:cm}}}}}$

——————————————————————————————

${\pink {\underline {\bf {\pmb {Semiperimeter \:of\:the \:triangle(S)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {S=\dfrac{P}{2}}}}}}}}$

$\sf S=semiperimeter \:of\:the \:triangle$
$\sf P=perimeter \:of\:the \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies S=\dfrac{42}{2}$

$\bf \implies S=\dfrac{\cancel{42}}{\cancel{2}}$

$\implies {\blue {\boxed {\boxed {\purple {\sf S=21\:cm}}}}}$

——————————————————————————————

${\pink {\underline {\bf {\pmb {Area \:of\:the \:triangle(A)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {A_{(Triangle)}=\sqrt{S\Big(S-a\Big) \Big(S-b\Big) \Big(S-c\Big)}}}}}}}}$

$\sf A=area\:of \:the \:triangle$
$\sf S=semiperimeter \:of\:the \:triangle$
$\sf a=first \:side \:of\:the \:triangle$
$\sf b=second\:side \:of\:the \:triangle$
$\sf c=third \:side \:of\:the \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies A=\sqrt{21\Big(21-18\Big) \Big(21-10\Big) \Big(21-14\Big)}$

$\bf \implies A=\sqrt{21\Big(3\Big) \Big(11\Big) \Big(7\Big)}$

$\bf \implies A=\sqrt{21\times 3\times 11\times 7}$

$\bf \implies A=\sqrt{4851}$

$\bf \implies A=\sqrt{441\times 11}$

${\blue {\boxed {\boxed {\purple {\mathfrak {A=21\sqrt{11}\:{cm}^{2}}}}}}}$

${\underbrace {\red {\overline {\red {\underline {\red {\pmb {\sf {{\therefore} The\:area \:of \:the \:triangle \:is\:21\sqrt{11}\:{cm}^{2}}}}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

____________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Area \:of \:the \:triangle = \dfrac{1}{2}bh$

$\sf Perimeter\:of \:the \:triangle =a+b+c$

Find the area of a triangle.its two sides are 18cm and 10cm, perimeter is 42 cm

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