2D and 3D Shapes
Properties of 2D Shapes
Regular and irregular 2D shapes include the circle, triangle, square, rectangle, pentagon, and hexagon. Let us look at a few of them and their properties.
Circles –
Circles are entirely round shapes formed by a single curved line. The curved line’s points are at equal distances from its centre.
A semi-circle has two sides, one curved and one straight. The entire arc has a 180° angle.
Triangles (3 sides) –
A triangle is a closed polygon with three sides, three vertices, and three angles. The sum of the triangle’s three interior angles is 180°.
An equilateral triangle is a regular triangle with 60° angles each.
Any triangle with one right angle is referred to as a right-angled triangle.
A scalene triangle is an irregular triangle wherein every side and angle is unique.
An isosceles triangle has two equal sides and two equal angles.
Quadrilaterals (4 sides) –
A square is a regular quadrilateral with all vertices at 90° angles.
A kite has two sets of equal-length sides, with diagonals intersecting at right angles.
A rectangle is made up of two parallel straight lines, each with a 90° angle.
A rhombus is defined by two parallel lines, equal sides, and opposite equal angles.
A trapezium has one parallel pair of lines.
A parallelogram is made up of two parallel lines and two opposite equal angles.
Polygons (4+ sides) –
A 5-sided shape is called a Pentagon. Interior angles add up to 540°.
A 6-sided shape is called a Hexagon. Interior angles add up to 720°.
A 7-sided shape is called a Heptagon or Septagon. Interior angles add up to 900°.
An 8-sided shape is called an Octagon. Interior angles add up to 1080°.
A 9-sided shape is called a Nonagon. Interior angles add up to 1260°.
A 10-sided shape is called a Decagon. Interior angles add up to 1440°.
3D Shapes
A three-dimensional shape is defined in geometry as a solid figure or an item or shape with three dimensions — length, breadth, and height. In our day to day life, we see several objects around us which have different shapes. For example, books, balls, ice-cream cones etc. One thing common in these objects is that they all have some length, breadth and height or depth. Thus they have three dimensions and so are known as 3D shapes. The D in 3D stands for dimensional. 3D shapes occupy space. In a world with three dimensions, you can travel forward, backward, right, left, and even up and down.
Examples of 3D Shapes
Cuboid, cube, cylinder, sphere, pyramid and cone are a few examples of 3D shapes
Types of 3D Shapes
In mathematics and real life, there are many 3D shapes and objects with different bases, surface areas and volumes. Let us look at a few of the most commonly seen 3D shapes.
Sphere
A sphere is round and circular in shape. All the points on the surface of the sphere are equidistant from the centre. It has the following dimensions: radius, diameter, circumference, volume, and surface area. There is only one face, no edges, and no vertices. For example, a ball, lemon, etc.
Cube and Cuboid
The cube and cuboid have the same number of faces, vertices, and edges. The major distinction between a cube and a cuboid is that a cube has all six faces that are squares, whereas a cuboid has all six faces that are rectangles. For example, ice cube, Rubik’s cube, etc.
pentagonal prisms, hexagonal prisms, and so on.
Polyhedrons
A three-dimensional form having flat polygonal faces, straight edges, and sharp corners or vertices is known as a polyhedron. Polyhedrons are further classified into Prisms, Pyramids and Platonic Solids (Eg. Octahedron, Dodecahedron, Icosahedron).
3D Shapes Formulas
Every three-dimensional shape has a surface area and a volume metric. The surface area is the area occupied by the 3D shape at the bottom, top, and all faces, including any curved surfaces. A 3D shape’s volume is defined as the amount of space it takes up.
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