What is the area of an equilateral triangle with a side of ^@R \ | Math Question and Answer

Answer:

$\dfrac { R^2 \sqrt{ 3 } } { 4 } \space cm^2$

Step by Step Explanation:

As per Heron's formula, the area of a triangle with sides $a, b$ and $c$ and perimeter $2S = \sqrt{ S(S - a)(S - b)(S - c) }$
Here, $a = b = c = R$ and $S = \dfrac {3}{2} \times a = \dfrac { 3R } { 2 }.$
$\begin{align} \text { Therefore, Area } & = \sqrt { \dfrac { 3R } { 2 } \times (\dfrac { 3R } { 2 } - R) \times (\dfrac { 3R } { 2 } - R) \times (\dfrac { 3R } { 2 } - R) }\\ & = \sqrt { \dfrac { 3R } { 2 } \times \dfrac { R } { 2 } \times \dfrac { R } { 2 } \times \dfrac { R } { 2 } } \\ & = \dfrac { R^2 \sqrt{ 3 } } { 4 } cm^2 \end{align}$

You can reuse this answer
Creative Commons License

Chat with us