Question

The area of incircle of an equilateral triangle of side 42 cm is by brainly

Answer 1

HELLO!!

ANSWER:

AREA = 462cm²

EXPLANATION:

Radius of incircle=a2√3

=422√3

=7√3

Area of incircle =227∗49∗3

=462cm²

HOPE IT HELPS YOU!!

Answer 2

Given:

The side of the equilateral triangle ($a$) = $42\;cm$

To find:

The area of the incircle of an equilateral triangle

Formula:

Area of circle = $\pi r^{2}$

Area of triangle = $\frac12bh$

Area of equilateral triangle = $\frac{\sqrt3}4a^2$

Step-by-step explanation:

ABC is an equilateral triangle.

In ΔAOB, base (b) is 42 cm and height (h) is r

$ar(\triangle AOB)\;=\;\frac13\;ar(\triangle ABC)$

$\frac12\;\times\;42\;\times\;r\;=\;\frac13\;\times\;\frac{\sqrt3}4\;\times\;42\;\times\;42$

$r\;=\;7\sqrt3$ $cm$

⇒ The required area of incircle = $\pi r^{2}$

⇒ $\frac{22}7\;\times\;7\sqrt{3\;}\;\times\;7\sqrt3$

⇒ $154\;\times\;3$

⇒ $462\;cm^{2}$

Answer:

The area of the incircle of an equilateral triangle of side 42 cm is $462\;cm^{2}$