Question

15. The height of an equilateral triangle is √6 cm. Its area is
(a) 3√3 cm2 (b) 2√3 cm2 (c) 2√2 cm2 (d) 6√2 cm2​

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• Height of equilateral triangle =$\sf{\sqrt{6}}$

$\Large\underline{\underline{\sf To\:Find:}}$

• Area of equilateral triangle.

$\Large\underline{\underline{\sf Formula\:Used:}}$

${\boxed{\boxed{\sf \pink{Area\:of\: equilateral\: triangle=\dfrac{\sqrt{3}}{4}a^2}}}}$

$\Large\underline{\underline{\sf Solution:}}$

☄ Applying Pythagoras Theorem

hypotenuse (h) = a cm

perpendicular (p) = √6 cm

base (b) = a/2

h² = p² + b²

$\implies{\sf a^2=(\sqrt{(6)}^2+(\left(\dfrac{a}{2}\right)^2 }$

$\implies{\sf a^2=6+\dfrac{a^2}{4} }$

$\implies{\sf a^2-\dfrac{a^2}{4}=6}$

$\implies{\sf \dfrac{4a^2-a^2}{4}=6 }$

$\implies{\sf \dfrac{3a^2}{4}=6}$

$\implies{\sf a^2=\dfrac{6×4}{3} }$

$\implies{\sf a^2=8cm^2}$

☄Area of equilateral triangle

$\Large{\sf A=\dfrac{\sqrt{3}}{4}a^2}$

$\implies{\sf A=\dfrac{\sqrt{3}}{4}×8cm^2}$

$\implies{\sf A=2\sqrt{3}cm^2 }$

$\Large\underline{\underline{\sf Answer:}}$

Option (b) $\bf{2\sqrt{3}cm^2}$

•°• Area of equilateral triangle is $\sf{2\sqrt{3}cm^2}$.

Answer 2

$\huge\mathcal\pink{♡Añswer♡}$

Given:

Height of equilateral triangle =$\sf{\sqrt{6}}$

$\Large\underline{\underline{\sf To\:Find:}}$

Area of equilateral triangle.

$\Large\underline{\underline{\sf Formula\:Used:}}$

${\boxed{\boxed{\sf \pink{Area\:of\: equilateral\: triangle=\dfrac{\sqrt{3}}{4}a^2}}}}$

$\Large\underline{\underline{\sf Solution:}}$

☄ Applying Pythagoras Theorem

hypotenuse (h) = a cm

perpendicular (p) = √6 cm

base (b) = a/2

h² = p² + b²

$\implies{\sf a^2=(\sqrt{(6)}^2+(\left(\dfrac{a}{2}\right)^2 }$⟹

$\implies{\sf a^2=6+\dfrac{a^2}{4} }$⟹

$\implies{\sf a^2-\dfrac{a^2}{4}=6}$⟹

$\implies{\sf \dfrac{4a^2-a^2}{4}=6 }$⟹

$\implies{\sf \dfrac{3a^2}{4}=6}$⟹

$\implies{\sf a^2=\dfrac{6×4}{3}}$⟹

$\implies{\sf a^2=8cm^2}$⟹

☄Area of equilateral triangle

$\Large{\sf A=\dfrac{\sqrt{3}}{4}a^2}$

$\implies{\sf A=\dfrac{\sqrt{3}}{4}×8cm^2}$⟹

$\implies{\sf A=2\sqrt{3}cm^2 }$⟹

$\Large\underline{\underline{\sf Answer:}}$

Option (b) $\bf{2\sqrt{3}cm^2}$

Area of equilateral triangle is$\sf{2\sqrt{3}cm^2}$

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