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## Formulas to find Area of Rectangle, Square, Parallelogram, Triangle, Circle, etc.

**TIPS FOR SOLVING QUESTIONS RELATED TO AREA:**

1. Area of Square = (side) Perimeter of Square = 4 x side 2. Area of Rectangle = Length x Breadth Perimeter of Rectangle = 2(Length + Breadth) 3. Area of 4 walls of a room = 2(Length + Breadth) x Height |

4. **Triangle:** A triangle is a a plane figure with three straight sides and three angles.

(i) Right triangle with base and height given.

\begin{aligned} \text{Area of a triangle =} \frac{1}{2}*Base*Height \\

\end{aligned}

(ii) Triangle with three different sides a, b and c.

\begin{aligned} \text{Area of a triangle =}\sqrt{s(s-a)(s-b)(s-c)}, \\

\end{aligned}

\begin{aligned}

s= \frac{1}{2}(a+b+c) \\

\end{aligned}

(iii) Equilateral triangle - A triangle with all three sides of equal length.

\begin{aligned} \text{Area of a equilateral triangle =}
\frac{\sqrt{3}}{4}*(side)^2

\end{aligned}

(iv). Radius of incircle of an equilateral triangle of side a = \begin{aligned} 5. |

6. **Circle:** A circle is a round plane figure whose boundary (the circumference) consists of points equidistant
from a fixed point (the centre).

(i) \begin{aligned} \text{Area of a circle} = \pi R^2 \end{aligned}, where R is radius of the circle

(ii) \begin{aligned} \text{Circumference of a circle} = 2 \pi R \end{aligned}

(iii) \begin{aligned} \text{Length of a arc} = \frac{2 \pi R \theta }{360} \\

\text{ where } \theta \text{ is the central angle } \end{aligned}

(iv)

\begin{aligned} \text{Area of sector = } \frac{1}{2}(arc* \theta) \\

= \frac{\pi R^2 \theta}{360}

\end{aligned}

(v)

\begin{aligned} \text{Area of a semi circle =} \frac{\pi R^2}{2} \end{aligned}

(vi)

\begin{aligned}\text{Circumference of a semi circle =} \pi R \end{aligned}