In geometry, a shape can be defined as the form of an object or its outline, outer boundary or outer surface.

There are different shapes in math.

Circle semi-circle

Square Rectangle

Parallelogram Decagone

Nine sided shape Trapezium

Kite Pentagone

Hexagone Heptagone

Rhombus Octagon

Circle

All points are the same distance from the center.

In Maths or Geometry, a **circle** is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the centre. The distance from the centre of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice the radius.

A circle is a basic 2D shape which is measured in terms of its radius. The **circles** divide the plane into two regions such as interior and exterior regions. It is similar to the type of line segment. Imagine that the line segment is bent around till its ends join. Arrange the loop until it is precisely circular.

The **Radius** is the distance from the center outwards.

The **Diameter** goes straight across the circle, through the center.

The **Circumference** is the distance once around the circle.

### Circle Shaped Objects

There are many objects we have seen in the real world that are circular in shape. Some of the examples are:

- Ring
- CD/Disc
- Bangles
- Coins
- Wheels
- Button
- Dartboard
- Hula hoop

We can observe many such examples in our day-to-day life.

Nonagone

What is nine sided shape

A nonagon is a polygon made up of 9 sides and 9 angles.

Nonagon = Nona + gon where Nona means nine and gon means sides.

Angles of a nonagon:

A nonagon consists of 9 angles. The sum of angles of a nonagon is 1260°.

A nonagon has 9 exterior angles. The sum of angles of the exterior angles of a nonagon is 360°.

Tyes of Nonagon

There are two types of nonagon.

Regular nonagon

A nonagon in which all sides are equal and all angles are equal is a regular nonagon.

Each angle of a regular nonagon is of 140°.

Irregular nonagon

A nonagon in which all sides are not equal and all angles are not equal. The measure of its angles is different but the total sum of all its interior angles is always 1260°.

Rectangle

A **rectangle** is a four-sided polygon having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

- Each internal angle is 90°.

Opposite sides are parallel and of equal length (so it is a Parallelogram). |

## Area of a Rectangle

Area = a × b

### Example: A rectangle is 6 m wide and 3 m high. What is its Area?

Area= 6 m × 3 m

= **18 m**^{2}

## Perimeter of a Rectangle

The perimeter is the distance around the edges.

The Perimeter is **2 times (a + b)**:

Perimeter = 2(a+b)

### Example:

### A rectangle is 12 cm long and 5 cm tall. What is its Perimeter?

Perimetre= 2 × (12 cm + 5 cm)

= 2 × 17 cm

= **34 cm**

Other names of the rectangle

- Since all the angles of a rectangle are equal, we also call it an equiangular quadrilateral.
- Since it has parallel sides, we can also call it a parallelogram. A parallelogram is a quadrilateral whose opposite sides are equal and parallel.

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Properties of a rectangle:

- It is a flat shape.
- It has 4 sides (edges).
- It has 4 corners (vertices).
- It has 4 right angles.

Square

A square is a flat shape with 4 equal sides and every angle is a right angle (90°). *The little squares in each corner mean “right angle”.*

All sides are equal in length | |

Each internal angle is 90 degree | |

Opposite sides are parallel (so it is a Parallelogram).Area of a square The Area is the side length squared:Area = a × aExample: A square has a side length of 6 m. What is its area?Area = 6 m × 6 m = 36 m^{2} The area is also ^{}half of the diagonal squaredPerimeter of a SquareThe perimeter is the distance around the edge. The perimeter is 4 times the side length:Perimeter = 4aExample: A square has a side length of 12 cm. What is its Perimeter?Perimeter = 4 × 12 cm = 48 cm |