Question

find the area of a triangle two sides of which are 18 cm and 10cm and the perimeter is 42cm​

Answer 1

Given :

• Perimeter of triangle = 42 cm
• 1st side of triangle = 18 cm
• 2nd side of triangle = 10 cm

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To Find :

• Area of Traingle = ?

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Solution :

~ Formula Used :

• Perimeter :

${\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Perimeter{\small_{(Triangle)}} = a + b + c }}}}}$

• Area :

${\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Area{\small_{(Triangle)}} = \sqrt{s (s - a)(s - b)(s - c) } }}}}}$

Where :

• s = Semi - Perimeter
• a = Side 1
• b = Side 2
• c = Side 3

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~ Calculating the 3rd side of Triangle :

$\; \longmapsto \sf \; \; \; { Perimeter = a + b + c }$

$\; \longmapsto \sf \; \; \; \; \; \; { 42 = 18 + 10 + c }$

$\; \longmapsto \sf \; \; \; \; \; \; \; \; \; { 42 = 28 + c }$

$\; \longmapsto \sf \; \; \; \; \; \; \; \; \; { 42 - 28 = c }$

$\; \; \; \; {\orange{\longmapsto \: {\underline{\underbrace{\sf{ 3rd \: Side = {\color{maroon}{\sf{ 14 \: cm }}}}}}}}}$

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~ Calculating the Area of Triangle :

• Semi - Perimeter :

$\; \longrightarrow \sf \; \; \; { S = \dfrac{a + b + c}{2} }$

$\; \longrightarrow \sf \; \; \; { S = \dfrac{18 + 10 + 14}{2} }$

$\; \longrightarrow \sf \; \; \; \; \; \; \; \; \; { S = \dfrac{42}{2} }$

$\; \longrightarrow \sf \; \; \; \; \; \; \; \; \; { S = \cancel\dfrac{42}{2} }$

$\; \; \; \; {\blue{\longrightarrow \: {\underline{\underbrace{\sf{ Semi - Perimeter = {\color{red}{\sf{ 21 \: cm }}}}}}}}}$

• Area :

$\; \dashrightarrow \sf \; \; \; \; { Area{\small_{(Triangle)}} = \sqrt{s (s - a)(s - b)(s - c) } }$

$\; \dashrightarrow \sf \; \; \; \; { Area{\small_{(Triangle)}} = \sqrt{21 (21 - 18)(21 - 10)(21 - 14) } }$

$\; \dashrightarrow \sf \; \; \; \; { Area{\small_{(Triangle)}} = \sqrt{21 \times 3 \times 11 \times 7 }}$

$\; \dashrightarrow \sf \; \; \; \; { Area{\small_{(Triangle)}} = \sqrt{ 7 \times 3 \times \sqrt{11} }}$

$\; \; \; \; {\pink{\dashrightarrow \: {\underline{\underbrace{\sf{ Area = {\color{orange}{\sf{ 21 \sqrt{11} \: cm² }}}}}}}}}$

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❝ Area of the triangle is 21√11 cm² . ❞

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Answer 2

Answer:

Formula is in short!

hope it helps you.