Question

The sides of a triangle are 12cm, 16cm and 20cm, find its area

Answer 1

Question :- The sides of a triangle are 12cm, 16cm and 20cm . find its area ?

Solution :-

we have given that, sides of a triangle are 12cm, 16cm and 20cm.

So,

→ Perimeter of ∆ = (12 + 16 + 20) = 48 cm.

→ Semi - Perimeter = 48/2 = 24 cm.

then,

→ Area of ∆ = √[s*(s-a)*(s-b)*(s-c) , where s is semi - perimeter and a , b and c are length of sides of ∆ .

Putting values we get,

→ Area of ∆ = √[24 * (24 - 12) * (24 - 16) * (24 - 20)]

→ Area of ∆ = √(24 * 12 * 8 * 4)

→ Area of ∆ = √(2 * 12 * 12 * 2 * 4 * 4)

→ Area of ∆ = √(2² * 12² * 4²)

→ Area of ∆ = 2 * 12 * 4

→ Area of ∆ = 96 cm².

Hence, Area of triangle will be 96 cm².

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Answer 2

Given:-

• 1st side - 12 cm
• 2nd side - 16cm
• 3rd side - 20cm

To find:-

• Area of this triangle

Formula:-

• Herons formula

$\underline{\boxed{\sf Ar(Δ) = √s(s-a)(s-b)(s-c)}}$

solution:-

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

S = $\sf\dfrac{12+16+20}{2}$

S = $\sf\dfrac{48}{2}$ = 24

Ar(Δ) = √24(24-12)(24-16)(24-20)

Ar(Δ) = √24×12×8×4

Ar(Δ) = √2×2×2×3×2×2×3×2×2×2×2×2

Ar(Δ) = 2×2×2×2×2×3

Ar(Δ) = 96 cm²

hence, the required area is 96cm²

Additional Information

to find the area of an equilateral triangle, the following formula is used:-

⇒$\underline{\boxed{\sf Ar(Δ) = \dfrac{√3}{4}a²}}$

to find the area of a right-angled triangle, the following formula is used:-

⇒$\underline{\boxed{\sf Ar(Δ) = \dfrac{1}{2}base×height}}$