# 7th Class Mathematics Perimeter and Area

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

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