# Area and Perimeter

## What is Area?

The area is the amount of two-dimensional space taken up by the object. It is measured in square units.The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape. The area of all the shapes depends upon their dimensions and properties. Different shapes have different areas.

### Formulas for Finding Area

- Area of the rectangle = length × width
- Area of the Square = s², where ‘s’ = sides of the square
- The area of a triangle is A = $\frac{1}{2}$ b × h where’ b’ is the base and ‘ h’ is the height
- Area of the circle = πr² where ‘ r ‘ is the radius
- The area of the parallelogram is A = b × h; here b = base and h =vertical height
- Area of parallelogram = base × height
- Area of rhombus = base × height
- The Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)

## What is Perimeter?

The perimeter is the distance around the object. Perimeter of a shape is defined as the total distance around the shape. The perimeter is the length of the fence. A perimeter is a total distance that encompasses a shape, in a 2d plane. The units of the perimeter are, cm, m etc.

### Formulas for Finding Perimeter

- Perimeter of Rectangle: We can see that in the rectangle the two sides are parallel and equal and also all the angles are 90 degrees. P = l+ b+ l+ b = 2l + 2b = 2 ( l + b )

- Perimeter of Square: So a rectangle with all its sides equal is a square. A perimeter of a square is 4 × S
- The Perimeter of a Triangle: is given by P = (a + b + c), where a, b and c are the 3 sides of the triangle.
- Perimeter of Parallelogram = 2 (sum of adjacent sides)
- Perimeter of Rhombus = 4 × side

### Area and Circumference of Circle

**Area of Circle** refers to the measure of the two-dimensional space enclosed within the circular boundary. Area of Circle is determined by the size of the circle’s radius. The radius is the distance from the center of the circle** **to any point on its boundary. it is measured in square units.

**Area of Circle Formula :**

Area of Circle = πr^{2}

Area of Circle = πd^{2 }/ 4

where,**r** is radius**d** is diameter**π** = 22/7 or 3.14

Area of circle formula is useful for measuring areas of circular fields or plots. It is also useful to measure the area covered by circular furniture and other circular objects.

## Parts of a Circle :

Circle is a closed curve in which all the points are equidistant from one fixed point i.e. **centre**.

**Radius:** The distance of a point from the boundary of the circle to its centre is termed its radius. Radius is represented by the letter ‘**r**‘ or ‘**R**‘. The area and circumference of a circle are directly dependent on its area.

**Diameter:** Longest chord of a circle that passes through its centre is termed its diameter. It is always twice its radius.

**Diameter formula:** The formula for the diameter of a circle is Diameter = 2 × Radius

**d = 2×r or D = 2×R**

**Circumference:** The circumference of the circle is the total length of its boundary i.e. perimeter of a circle is termed its circumference. The Circumference of a circle is given by the formula **C = 2πr**.

## Area of a Sector of a Circle

Area of a sector of a circle is the space occupied inside a sector of a circle’s border. A semi-circle is likewise a sector of a circle, where a circle has two equal-sized sectors.

**A = (θ/360°) × πr**^{2}

where,**θ **is the sector angle subtended by the arcs at the center (in degrees),**r **is the radius of the circle.

### Area of Quadrant of a circle

A quadrant of a circle is the fourth part of a circle. It is the sector of a circle with an angle of 90**°**.

**Area of Quadrant = (90°/360°) × πr**^{2}** = πr**^{2}** / 4**