[Maths Class Notes] on 2D and 3D Figures Pdf for Exam

Geometry is a study of shapes. It is broadly classified into two types: plane geometry called 2d shapes and solid geometry called 3d shapes. Let us draw a picture of a notebook on a piece of paper. What we observe is a plain picture drawn on paper. It does not occupy any space called 2d shapes, but if we keep a real notebook on that piece of paper it occupies some space, and such shapes are called 3d shapes or three-dimensional shapes. 

Plane geometry or two-dimensional geometry deal with the flat figures that can be drawn on a piece of paper like line, curves, polygons, quadrilaterals, etc, while solid geometry or three-dimensional geometry deals with solid shapes or three-dimensional shapes. Examples of three-dimensional shapes are sphere, cylinders, cones, etc. 

What are 2D Shapes?

In geometry, a shape or a figure that has two dimensions namely a length and a breadth is called a 2D shape. In other words, a plane object that has only length and breadth is a 2 dimensional shape. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides.

There are no fixed properties of the 2D shape. As each shape has a different number of sides and for each shape, properties vary. But, every 2D shape is flat and is enclosed.

Definition of 2D Shapes 

In geometry, 2D shapes can be defined as completely flat plane figures and only two dimensions – length and width. They are not thick and can only be measured in two dimensions. A polygon is a 2-Dimensional shape composed of vertical line segments connected to one another, thus giving it a closed shape. Circles, squares, rectangles, and triangles are some examples of two-dimensional objects and these shapes can be drawn on paper. Except for the circle which is a curved figure, all 2-D shapes have sides, corners, and internal angles. 2D Figures have at least three 2D straight sides and they are known as polygons and that includes triangles, squares, and quadrilaterals.

What are 3D Shapes?

The shapes that occupy space are called 3D shapes. 3D shapes can also be defined as the solid shapes having three dimensions length, width, and height. A football is an example of the sphere which is a three-dimensional figure while a circle drawn on a piece of paper is a two- dimensional figure. Similarly, we have many 3D shapes all around us like a table, chair, notebook, pen, etc.

Definition of 3D Shapes

3D shapes are solid objects or objects with three dimensions (length, width, and height), compared to objects with only two sides in length and width. The most important terms with the geometric shapes of 3D are faces, edges, and vertices. They have a depth so they take a certain amount of volume. Some 3D shapes have their base and top parts or cross sections such as 2D shapes. For instance, The cube has all the square-shaped sides. Now we will learn more about each 3D shape. 3D environments are divided into several categories. Some of them have curved areas; others are in the form of pyramids or prisms.

Terms Used For 3D Figures

• Face. The face is a flat or curved area in 3D shape. For example a cube has six faces, a cylinder has three faces and a circle has one face.

• Edges. Edge is the corner where two points meet .

• Vertices. The vertex is where the edges meet.

Difference Between 2D and 3D Shapes: Tabular Form

Solved Examples:

Example 1:

Find the volume and surface area of a cuboid of l= 10cm, b = 8cm and h = 6 cm.

Solution: 

We have Volume of cuboid = V = l x b x h 

= 10 x 8 x 6

= 480cm2

Surface area = 2 ( lb + lh + bh)

= 2( 10×8 + 10×6 + 8×6)

= 2(80 + 60 + 48)

= 376cm2

Example 2:

The length of the rectangular field is 15m and width is 6m. Find the area and perimeter of the field.

Solution:

Given that   Length = 15m

Width = 6m

We have,  Area formula A = length x width 

= 15 x 6 

= 90 m2

And Perimeter formula P = 2 (length + width) 

= 2 x (15 + 6) 

= 2 x 21

= 42 m.

Quiz Time

1.Find the area of the right-angled triangle whose base is 12cm and hypotenuse 13cm.

1. 40 cm

2. 85 cm

3. 60 cm

4.  30cm2

2. The side of a square whose surface area is 600cm is

1. 10cm

2. 20 cm

3. 30 cm

4. 40 cm

Fun Facts