11 Plus 2D and 3D Shapes
Geometry is the most interesting, easy and most used part of mathematics. It may be any field we will be using geometry like construction, machine-building, even rocket sciences use it. 2D and 3D shapes are considered to be the most important parts of geometry. Here D indicates dimension. The 2D shape is a 2 Dimensional shape, which lies on a plane (an infinite imaginary sheet). If we add width to the 2D, we get 3D shapes. Some examples of 2D shapes are Triangle, Square, Circle etc. if we add something like width or height to them, they turn to 3D. If we add height to the square, it turns to Cube; similarly, if we add height to circle, it turns to Cylinder. Some other 3D shapes are cone, pyramid, cuboid, etc.. 2D and 3D shapes are 11 plus geometry.
Considering 2D shapes initially, we will learn many interesting things about these shapes right from the basics.
Let’s have a glance at some of the shapes,
The above-shown shapes are some examples of 2d shapes. If we observe them clearly, except the circle remaining are made of line segments (the line segment is a part of the line with two endpoints), the circle is not made of line segments but made of arcs.
Do you know you can draw any 2D shape by tracing out the object you have, like a book, food cans?
Exercise: Observe the figure and try to find out the shapes from it.
From the above figure, we can find 2 circles (eyes), a triangle (nose), and two rectangles (face and mouth). So it is easy to make some funny faces with these basic shapes, so what are you waiting for? Take a paper and try to draw some pictures using 2D shapes.
Let’s know about them and their properties in detail simply and effectively, starting with a circle.
Circles: A circle is a 2D shape in which all points lying on the edge of the circle are at the same distance from the centre—the important parameters of circle diameter, radius, chord, centre, etc.
In the above figure point, O is known as the centre, AB is known as Diameter, PQ is known as Chord and OR is known as the circle's radius.
- A line segment connecting any two points on the circle is known as a chord. The chord passing through the centre of the circle is known as diameter.
- The diameter is said to be the longest chord of the circle.
- We can have an infinite number of Diameters in a circle.
- Every diameter is a chord, but every chord need not be the diameter.
- The diameter divides the circle into two halves, and each half is known as Semicircle.
- A line segment connecting the centre and any point on the circle is known as the circle's radius.
- Each diameter has two radii (plural form of radius).
- Every circle has an infinite number of Radii.
- If the radius is 0, then it is called a Point Circle.
- If the radius is one, then it is called a Unit Circle.
- Two circles with a common centre and different radii are said to be Concentric Circles.
The circle area is considered the space occupied by the circle, and the perimeter is considered the boundary of the circle and sometimes called the length of the circle.
Hence perimeter of the circle is 132 cm.
The other shapes made of a Line segment are called Polygons. Polygons are defined as the closed shapes made of line segments. Based on the number of line segments used, polygons have names. Suppose three-sided polygons are known as Triangles, four-sided one is called Quadrilateral etc.
Note: The perimeter of any polygon is just the sum of all the sides of that polygon. For example, a, b and c are the sides of the triangle, and its perimeter is a+b+c
The polygons Triangle and Quadrilateral are mostly used, so let’s learn about them in detail.
Triangle: Triangle is a three-sided polygon the name TRI ANGLE itself indicates it is a three-sided shape, with three angles (rotation made by any of 2 adjacent sides). They can be classified into many types based on sides and angles.
Types of Triangles
Based on the sides:
- Equilateral Triangle
- Isosceles Triangle
- Scalene Triangle
Based on Angles:
- Right-angled triangle
- Obtuse angled triangle
- Acute angled triangle
- The triangle area is given by (1/2) x bxh where b = base, h = height.
Quadrilaterals: Four-sided polygon is called a Quadrilateral. Quad means 4. Some of the examples of quadrilaterals are square, rectangle, rhombus, trapezium, parallelogram etc...
Let’s know about the area of the above-mentioned Quadrilaterals.
- The area of a square of side ‘a’ is A = axa.
- Area of Rectangle of length l, breadth b is A = lxb.
- The area of Rhombus of diagonals p and q is A = (pxq) /2.
- Area of Parallelogram of side b and height h is A = bxh.
- Area of Trapezium of parallel sides a, b and height h is A = (a+b)/2 x h.
They are 3-dimensional shapes that have width extra. The 3D shape of the square is Cube, the circle is Cylinder, and the rectangle is Cuboid.
Let’s see some examples of 3D shapes.
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