Question

find the area of an equilateral triangle with side 2 √3cm.​

Answer 1

Step-by-step explanation:

Answer:

The area of the given equilateral triangle with side 2 \sqrt{3} \mathrm{cm}2

3

cm is 3 \sqrt{3} c m^{2}3

3

cm

2

Solution:

Equilateral triangle: The triangle which has equal sides. It is also known as equiangular i.e. all the internal angles are congruent to each other with 60^{\circ}60

∘

The triangle given is an equilateral triangle so, the three sides of the triangle are same which is a=2 \sqrt{3} \mathrm{cm}a=2

3

cm

\text { area of equilateral triangle } A=\frac{\sqrt{3}}{4} a^{2} area of equilateral triangle A=

4

3

a

2

\therefore A=\frac{\sqrt{3}}{4}(2 \sqrt{3})^{2}∴A=

4

3

(2

3

)

2

A=\frac{\sqrt{3}}{4} \times 2 \sqrt{3} \times 2 \sqrt{3}A=

4

3

×2

3

×2

3

A=\frac{4 \times 3 \times \sqrt{3}}{4}=3 \sqrt{3}A=

4

4×3×

3

=3

3

The area of the triangle is 3 \sqrt{3} c m^{2}3

3

cm

2

Answer 2

Given that,

Side of an equalateral triangle = 2√3 cm

Area of triangle = ?

we know that,

• Area of an equalateral triangle = √3/4 × a²
• Area = √3/4 × (2√3)²
• Area = √3/4 × 4×3 cm²
• Area = 3√3 cm².

Therefore, the area of the equalateral triangle is 3√3 cm²

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