Question

the altitude of equalaterial triangle is 3√3.find it's area.​

Answer 1

sin60=perpendicular/hypotenuse

let hypotenuse or side of triangle be x

where perpendicular= altitude if equilateral triangle

and hypotenuse =side of equilateral triangle

under root 3/2=3under root 3/x

by cross multiplication x/2 = 3under root 3/under root 3

（ under root 3 cancelled on both side）

so x= 2 multiplied by 3

x=6

hence the side of equilateral triangle is 6 units

Answer 2

QUESTION:

the altitude of equalaterial triangle is 3√3.find it's area.

ANSWER:

We use the formula here;

Height of an equilateral triangle =

$\red{\frac{ \sqrt{3} }{2} \times side}$

Area of equilateral triangle =

$\pink{\frac{ \sqrt{3} }{4} \times {side}^{2}}$

now come to main question;

Altitude of equalaterial triangle =

$3 \sqrt{3} = \frac{ \sqrt{3} }{2} \times side \\ 2 \times 3 \sqrt{3} = \sqrt{3} \times side \\ \frac{6 \sqrt{3} }{ \sqrt{3} } = side \\ 6 = side$

$\huge\blue{6 \: units = side}$

now using the area formula;

$\frac{ \sqrt{3} }{4} \times {6}^{2} \\ \frac{ \sqrt{3} }{4} \times 36 \\ 9 \sqrt{3} {unit}^{2}$

area =

$\huge\green{9 \sqrt{3} {unit}^{2} }$

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