Perimeter and Area

**Category : **7th Class

**Perimeter and Area**

- Perimeter is the distance around a closed figure.
- Area is the part of plane occupied by the closed figure.

(a) Perimeter of a square= 4\[\times \]side units

(b) Perimeter of a rectangle = 2\[\times \](length + breadth) units

(c) Area of a square = side \[\times \] side sq. units

(d) Area of a rectangle = length \[\times \] breadth sq. units

- Area of a parallelogram = base \[\times \] height sq. units
- Area of a triangle =\[\frac{1}{2}\](area of the parallelogram generated from it)

= \[\frac{1}{2}\] \[\times \]base \[\times \] height sq. units

- Area of a trapezium =\[\frac{1}{2}\](a + b) h sq. units, where \['a'\]and \['b'\] are lengths of parallel sides and 'h' is the height.

- A circle is a closed curve in a plane drawn in such a way that every point on it is at a constant distance (r units) from a fixed point 0 inside it.

The fixed point 0 is called the **centre** of the circle and the constant distance r is called the **radius **of the circle.

**Circumference of a Circle:**The perimeter of a circle is called its circumference.- Circumference =\[2\pi r\] =\[\pi \]d, where r = radius and d = diameter.

Here \[\pi \](Pi) is a constant, equal to 3.14 approximately.

**Area of a Circle:**Area of a circle with radius r units is equal to \[\pi {{r}^{2}}\] sq units.**Area of a Ring:**

- The region enclosed between two concentric circles of different radii is called a ring.

Area of path formed between two concentric circular regions \[=\left( \pi {{R}^{2}}-\pi {{r}^{2}} \right)\] sq. units

\[=\pi \left( {{R}^{2}}-{{r}^{2}} \right)\]square units

\[=\pi \left( R+r \right)\left( R-r \right)\]square units

*play_arrow*Perimeter and Area

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