Question

The side of equilateral triangle is 4 cm, and then its area is
A. 16√3cm
B. 64√3cm
C. 4√3cm
D. 16cm²​

Answer 1

Equilateral Triangles

The formula to calculate the area of an equilateral triangle is given as,

$\boxed{\bf{Area_{(Equilateral \: triangle)} = \dfrac{\sqrt{3}}{4}a^2}}$

Where, a denotes side or edge of the equilateral triangle.

According to the question, the given side of equilateral triangle is 4cm. i.e. a = 4cm.

By substituting the given value in the formula, we get;

$\implies \rm{Area_{(Equilateral \: triangle)}} = \dfrac{\sqrt{3}}{4}(4)^{2} \\ \\ \implies \rm{Area_{(Equilateral \: triangle)}} = \dfrac{\sqrt{3}}{ \cancel{ \: 4 \: }} \times \cancel{16} \\ \\ \implies \rm{Area_{(Equilateral \: triangle)}} = \sqrt{3} \times 4 \\ \\ \implies \boxed{\bf{Area_{(Equilateral \: triangle)}} = 4\sqrt{3}}$

Hence, the area of equilateral triangle is 4√3cm. So, option (c) 4√3cm is correct.

$\rule{90mm}{2pt}$

IMPORTANT NOTES

• An equilateral triangle has 3 sides or edges.

• An equilateral triangle has 3 angles.

• All three sides of equilateral triangle are equal.

• All three angles of equilateral triangle are congruent and are equal to 60 degrees.

• Each interior angle of an equilateral triangle is 60 degree.

• Each exterior angle of an equilateral triangle is 60 degree.

• The sum of all three angles of an equiangular triangle is equal to 180 degrees. This is called the angle sum property of triangle.

• Perimeter of equilateral triangle is equal to 3 times of side length. i.e 3a. Where, a denotes side or edge of the equilateral triangle.

• Area of equilateral triangle is √3/4a². Where, a denotes side or edge of the equilateral triangle.