Question

If the height of the equilateral triangle is √3,then the area of the triangle is??????​

Answer 1

Answer:

Given ,

height = √3

We know that ,

height = √3 / 2 a

√3 = √3 / 2 a

a = 2

Area of equilateral triangle = √3/4 a²

Δ = √3/4 × 2²

Δ = √3/4 × 4

Δ = √3

Hence , area of the triangle is √3 unit²

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Answer 2

Answer:

The Area of the Equilateral Triangle is √3 (unit)²

Step-by-step explanation:

Equilateral triangle is the triangle which has three equal sides.

Let the side of the given Equilateral Triangle is "a".

Then the Height of the Equilateral Triangle will be

$area = \frac{ \sqrt{3} }{2} \: {side}^{2}$

or,

$\frac{ \sqrt{3} }{2} \times a$

Given that, the height of the equilateral triangle = √3

According to question,

$\frac{ \sqrt{3} }{2 } \times a = \sqrt{3}$

or,

$a = \frac{2}{ \sqrt{3} } \times \sqrt{3}$

or,

$a = 2 \: unit$

The area of the equilateral triangle is given by

$area = \: \frac{ \sqrt{3} }{4} \times \: {side}^{2}$

or,

$area = \: \frac{ \sqrt{3} }{4} \times \: {a}^{2}$

putting the value of "a" we get,

$area = \frac{ \sqrt{3} }{4} \times {2}^{2}$

or,

$area = \frac{ \sqrt{3} }{4} \times 4$

or,

$area = \sqrt{3} \: {unit}^{2}$

Conclusion:

The Area of the Equilateral Triangle is found to be √3 (unit)².