Question

Find the area of triangle whose sides are 12 cm,8cm and 10 cm.​

Answer 1

Answer :

• Area of triangle = 15√7 cm²

Given :

• Sides are 12cm , 8cm and 10cm

To find :

• Area of triangle

Solution :

Given,

• a = 12cm
• b = 8cm
• c = 10cm

To find the area of triangle first we need to find the semi perimeter of triangle then after we must to find the heron's formula then we get answer

We know that

• S = a + b + c / 2

Where , a , b and c are sides and s is semi perimeter of triangle

➞ s = a + b + c / 2

➞ s = 12 + 8 + 10 / 2

➞ s = 30/2

➞ s = 15cm

We know that,

Area of triangle by heron's formula,

• √s(s - a) (s - b) (s - c)

Where, s is semi perimeter of triangle (15cm) and a, b c are sides (12cm , 8cm , 10cm)

➞ √s(s - a) (s - b) (s - c)

➞ √15(15 - 12) (15 - 8) (15 - 10)

➞ √15(3) (7) (5)

➞ √15 × 3 × 7 × 5

➞ √1575

➞ √25 × 63

➞ 5√63

➞ 5√(3 × 3 × 7)

➞ 5 × 3√7

➞ 15√7 cm²

Hence , Area of triangle = 15√7 cm²

Answer 2

Given Sides of Triangle :

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• a = 12cm
• b = 8cm
• c = 10cm

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$\red{\bigstar}\:$The formula for finding the area of a triangle is$\sf{\:{\dfrac{1}{2}}\:\times\:b\:\times\:h.\:}$But no height is given so we'll use heron's formula.

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$\red{\bigstar}\:$For that, first we need to find the semi - perimeter of the triangle. Also denotes as 's'.

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We Know,

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• $\sf\blue{s\:=\:{\dfrac{a\:+\:b\:+\:c}{2}}}$

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$\:\:\:\:\:\dashrightarrow\:\sf{s\:=\:{\dfrac{8\:+\:10\:+\:12}{2}}}$

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$\:\:\:\:\:\dashrightarrow\:\sf{s\:=\:\cancel{\dfrac{30}{2}}}$

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$\:\:\:\:\:\dashrightarrow\:\sf{s\:=\:15cm}$

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$\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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• Area of Triangle by Heron's Formula:

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$\:\:\:\:\:\:\:\:\:\:{\bold{\dag}}\:{\sf{\underbrace{\purple{\sqrt{s(s\:-\:a)\:(s\:-\:b)\:(s\:-\:c)}}}}}$

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$\:\::\:\Longrightarrow\:\small\sf{\sqrt{15\:(15\:-\:8)\:(15\:-\:10)\:(15\:-\:12)}}$

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$\:\:\:\:\::\:\Longrightarrow\:\sf{\sqrt{15\:\times\:7\:\times\:5\:\times\:3}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\sqrt{3\:\times\:5\:\times\:7\:\times\:5\:\times\:3}}$

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$\:\:\:\:\::\:\Longrightarrow\:\sf{\sqrt{\underline{3\:\times\:3}\:\times\:{\underline{5\:\times\:5}\:\times\:7}}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{3\:\times\:5{\sqrt{7}}}$

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$\:\:\:\:\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{15{\sqrt{7}}{cm}^{2}}$

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$\:\:\:\therefore\:{\underline{\sf{Hence,\:Area\:of\:Triangle\:is\:{\sf{\bf{15{\sqrt{7}}{cm}^{2} }}}}}}.$

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