Question

Find the area of a triangle whose sides are 12cm,16 cmand 20 cm ​

Answer 1

Answer

The area of the triangle is 96 cm²

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Answer 2

Answer:

The area of the triangle is 96 cm².

Step-by-step explanation:

Sides of given triangle :

• $\sf{Side_1}$ = 12 cm
• $\sf{Side_2}$ = 16 cm
• $\sf{Side_3}$ = 20 cm

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★ Semi Perimeter :

$\boxed{\sf{Semi \: Perimeter = \frac{Side_1 + Side_2 +Side_3}{2}}}$

$\sf{\longrightarrow} \: Semi \: Perimeter = \dfrac{12 + 16 + 20}{2} \\ \\ \sf{\longrightarrow} \: Semi \: Perimeter = \dfrac{48}{2} \\ \\ \sf{\longrightarrow} \: Semi \: Perimeter = 24 \: cm$

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★ Using the Heron's Formula :

$\boxed{\sf{Heron's \: Formula = \sqrt{s(s - a)(s - b)(s - c)}}}$

• s = 24 cm
• a = 12 cm
• b = 16 cm
• c = 20 cm

$\sf{\longrightarrow{\sqrt{24(24- 12)(24 - 16)(24 - 20)}}}$

$\sf{\longrightarrow{\sqrt{24 \times 12 \times 8 \times 4}}}$

$\sf{\longrightarrow{\sqrt{12 \times 2 \times 12 \times 4 \times 2 \times 4}}}$

$\sf{\longrightarrow{12 \times 2 \times 4}}$

$\sf{\longrightarrow{12 \times 8}}$

$\sf{\longrightarrow{96 \: {cm}^{2}}}$

Area of triangle = 96 cm²

Therefore, the area of the triangle is 96 cm².