Question

Assertion: Area of an equilateral triangle of side ‘a’ is $=\frac{\sqrt{3}}{4}{a}^2$

Reason: The height of an equilateral triangle of side ‘a’ is $=\frac{\sqrt{3}}{4}{a}^2$

Which of the following is correct?

• A. A is true and R is false.
• B. A is false and R is true.
• C. Both A and R are true and R is the correct explanation of A.
• D. Both A and R are true but R is not the correct explanation of A.

Answer 1

The correct option is A

A is true and R is false.

If the side of an equilateral triangle is ‘a’ then by Heron’s formula:

Area of the triangle

$=\sqrt{\frac{3}{2}a(\frac{3}{2}a-a)(\frac{3}{2}a-a)(\frac{3}{2}a-a)}$

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

Where $\frac{3}{2}a$ is the semi - perimeter of the triangle.

If height of an equilateral triangle be h,

Then, $\frac{1}{2}\times a\times h=\frac{\sqrt{3}}{4}{a}^2$

$\therefore h=\frac{\sqrt{3}}{2}a$

$\therefore$ Assertion is true but reason is false.