Question

The length of altitude of a equilateral triangle of side a unit
(a)
$\sqrt{a} \times \frac{ \sqrt{3} }{2}$
${a}^{2} \times \frac{ \sqrt{3} }{4}$
${a}^{2} \times \frac{ \sqrt{3} }{2}$
None of these



Choose the correct answer And explain the reason for it ,



do it fast as possible, then only I will mark u as brainliest ​

Answer 1

Answer:

root 3/ 2 × a^2

because this the formula

Step-by-step explanation:

option c is correct

pls mark brainiest

Answer 2

Equilateral triangle

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.

Solution:

According to the question, the given length of side of an equilateral triangle is a units. i.e.

• a = a units.

By substituting the given value in the formula, we get the following result:

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

Therefore, the area of an equilateral triangle is $a^2 \times \frac{\sqrt{3}}{4}$. So, option (b) is correct.

$\rule{300}{2}$

Extra Information:

Some important properties and formulas of an Equilateral triangle:

• 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 $\frac{\sqrt{3}}{4}a^2$. Where, a denotes side or edge of the equilateral triangle.