Question

If the altitude of an equilateral triangle is √6 cm, its area is ______.
A. 2 √3 cm ²
B. 2√ 2 cm²
C. 3 √3 cm²
D. 6 √2 cm²

Answer 1

GIVEN: Triangle ABC is an equilateral triangle.

Altitude CM = √6

TO FIND THE AREA: of equilsteral triangle ABC

Here Sin60° ,= CM/CB

=> √3/2 = √6/CB

=> √3 CB = 2√6

=> CB = 2√6 / √3

=> CB = 2√2

=> AB = 2√2

Area( triangle ABC) = 1/2 * AB * CM

=> Area( triangle ABC) = 1/2 * 2√2 * √6

=> Area(triangle ABC) = √12 = 2√3


ANS: 2√3 square unit.

Answer 2

$ABC$ is an equilateral triangle

$AD=$ Altitude $=\sqrt{6}cm$

In right-angle △$ADB,$ Using Pythagoras theorem,

⇒ $(\frac{a}{2})^2+(\sqrt{6})^2=a^2$

⇒ $\frac{a^2}{4}+6=a^2$ ⇒ $\frac{3a^2}{4}=6$ ⇒ $a^2=8$ ⇒ $a=2\sqrt{2}cm$

∴ Δ$ABC$ (equilateral Δ) $=\frac{\sqrt{3} }{4} a^2=\frac{\sqrt{3} }{4}\times 2\sqrt{2}\times 2\sqrt{2}=2\sqrt{3}cm^2$