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Shapes in math


Shapes in math
Shapes in math

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.

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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°.
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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 m2

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 m2 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

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