Geometric Shapes

Shapes are an integral part of our everyday lives. From road signs and symbols to notebooks and baking trays, there are several geometric shapes around us. Geometry, which translates to “Earth measurement” is a branch of math that is related to the properties of shape and space. Geometry and geometric shapes are an important part of teaching math for kids. So, we’ve compiled a comprehensive list of all the geometric shapes that kids should know and their properties.

List of Geometric Shapes for Kids

So, what is a shape? A shape or figure is the external boundary, outline, form or surface of an object. Shapes can be 2 dimensional (2D) or 3 dimensional (3D). 2 dimensional shapes are those that have only 2 dimensions, length and width. A 3 dimensional figure is a solid shape or figure, which has 3 dimensions, length, width and height. Help your little one learn different shapes using these preschool shapes worksheets.

Here is a complete list of 2D and 3D geometric figures.

1. 2D Geometric Shapes

2 dimensional shapes are flat, plane figures that have only two dimensions, length and width. They are flat and have no depth, so they cannot be held physically. Some common 2D shapes are squares, rectangles, circles, pentagons, triangles, parallelograms etc. Here is a complete list of 2D geometric figures:

List of 2D Geometric Shapes:

• Triangles
• Quadrilaterals
• Concave and Convex Polygons
• Irregular and Regular Polygons
• Curved 2D Shapes

2. 3D Geometric Shapes

In geometry, 3 dimensional shapes are solid objects or figures that have 3 dimensions, length, width and height. Unlike 2D figures, 3D shapes can be held physically because they have depth or thickness. Cubes, cones, cylinders, pyramids, spheres etc are some examples of 3 dimensional shapes. Here is a list of some common 3D shapes:

List of 3D Geometric Shapes:

• Cylinder
• Cone
• Cube
• Cuboid
• Sphere
• Triangular Prism
• Square Pyramid
• Hexagonal prism
• Torus
• Icosahedron
• Dodecahedron
• Tetrahedron
• Octahedron
• Hexagonal Pyramid
• Pentagonal Prism
• Pentagrammic prism

Properties and Classification of 2D Geometric Figures

Triangles

A triangle is a closed 2 dimensional figure, which is 3-sided. It has three edges, three angles and three vertices. The sum of all the interior angles in a triangle adds up to 180^o. There are 13 different types of triangles based on their sides and angles. Triangles can be classified based on their angles, sides and both angles and sides. Here are the different types of triangles:

Triangles based on their sides:

• Equilateral triangle: A triangle with 3 equal sides or congruent sides is called an equilateral triangle. All the angles in an equilateral triangle measure 60^o.
• Scalene triangle: A scalene triangle is one that has two sides of the same length.
• Isosceles triangle: A triangle, which has no congruent sides and all the sides have different lengths, is called an isosceles triangle.

Triangles based on their angles:

• Right triangle: A triangle, which has one right angle (90^o) and two acute angles is called a right triangle.
• Acute triangle:  An acute triangle is one in which all the interior angles measure less than 90^o.
• Obtuse triangle: A triangle, which has one obtuse angle and two acute angles is called an obtuse triangle.

Triangles based on both sides and angles:

• Acute Equilateral Triangle: A triangle with 3 equal sides and 3 angles, which are less than 90^o is called an acute equilateral triangle.
• Obtuse Scalene Triangle: A triangle, which has one obtuse angle and unequal side lengths is called an obtuse scalene triangle.
• Right Isosceles Triangle: This is a triangle with one right angle and two equal sides. 
• Right Scalene Triangle: This is a triangle with 3 unequal sides and one right angle.
• Acute Scalene Triangle: This is a triangle with 3 unequal acute angles and 3 unequal sides.
• Acute Isosceles Triangle: This is a triangle with two equal acute angles and two equal sides.
• Obtuse Isosceles Triangle: This is a triangle with an obtuse angle and two equal sides.

For more information on triangles and learn how to find the area of a triangle, check out this triangle worksheet.

Quadrilaterals

Quadrilaterals are 2 dimensional, closed geometric figures that have 4 sides. They’re four-sided polygons, which have four edges and four vertices. The sum of all the angles in a quadrilateral adds up to 360^o. Quadrilateral shapes are classified based on their angles and side lengths. Here is a list of the different types of quadrilaterals and their properties:

Quadrilaterals based on their sides:

• Trapezium: A trapezium is a quadrilateral in which none of the sides are the same.
• Isosceles Trapezoid: A quadrilateral with equal base angles and non parallel sides.
• Kite:  A quadrilateral, which has two pairs of equal adjacent sides.
• Rhombus: A quadrilateral with four equal sides, opposite acute angles that are equal and opposite obtuse angles that are the same.

Quadrilaterals based on their angles:

• Rectangle: A quadrilateral with four right angles.

Quadrilaterals based on their parallels:

• Parallelogram: A parallelogram is a quadrilateral with 2 equal and parallel sides.
• Square: A quadrilateral with 4 right angles and 4 equal sides that are parallel to each other. Check out this square worksheet to know more about squares.
• Trapezoid: A quadrilateral, which has only one pair of parallel sides.

Want to learn more about rectangles? Then check out this rectangle worksheet, which helps you learn more about the geometric figure and find its area.

Concave and Convex Polygons

A polygon is a 2 dimensional, closed figure with three or more straight sides and angles. Triangles and quadrilaterals are both polygons. They can either be convex or concave in shape. 

Convex polygon: A polygon is convex-shaped when none of the line segments between each point goes inside. Additionally, all the vertices of a convex polygon point outside and away from the center. Each of the interior angles in a convex polygon measures less than 180^o. For example, triangles, parallelograms, rectangle, pentagon etc. 

Concave polygons: A concave polygon has at least one reflex angle greater than 180^o. In this geometric figure, at least two sides seem pushed inwards towards the center. Examples of concave polygons are concave hexagons, concave heptagon, star etc.

Irregular and Regular Polygons

Polygons can also be classified as regular and irregular polygons. 

Regular Polygon: In a regular polygon, all the sides are the same length and are symmetrically placed about the center. Additionally, all the angles are equal. Regular polygons are also convex. Some examples of regular polygons are squares, equilateral triangles, regular pentagon etc.

Irregular Polygons: These are polygons, which have unequal angles and sides. An irregular polygon can be convex or concave. For example, irregular pentagon, irregular hexagon, irregular octagon etc.

Curved 2D Shapes

Curved 2 dimensional shapes are circles, ellipses, crescents, parabolas, arcs etc. Here is a list of some common curved 2D shapes:

Circle

Circles are round, 2 dimensional geometric shapes, in which any point from the boundary is the same distance from the center. The boundary is continuous and has no corners or edges. 

Ellipse

An ellipse is a geometric figure that is a rounded shape like an oval or an egg. This geometric shape looks like a circle that has been stretched from the sides. 

Crescent

A crescent or lune is a shape that is formed when two circles overlap or intersect. For example, the moon has a crescent shape during the waxing and waning phases.

Properties and Classification of 3D Geometric Shapes

Here are the properties and classifications of some common 3 dimensional geometric shapes.

Cube

A cube is a solid, 3 dimensional geometric shape, which has 6 faces, 8 vertices and 12 equal edges. The 6 faces of a cube are square-shaped and all the sides have the same length. 

Cylinder 

A cylinder is a 3D figure, which has two circular bases parallel to each other. They’re connected by a curved surface at a fixed distance. A cylinder has 2 faces, 2 edges and no vertices.

Cuboid

This is a geometric figure, which has 6 faces, 12 edges and 8 vertices. Each of the faces in a cuboid is rectangular in shape.

Sphere

This is a round, 3 dimensional object that is shaped like a ball. Like in a circle, every point on the surface of the sphere is at the same distance from the center. Spheres have 1 face but no edges or vertices.

Cone

This is a 3 dimensional geometric figure that has a flat base joined to a point called the apex or vertex with a smooth, tapered, curved side. A cone has 2 faces, 1 flat and 1 curved surface and 1 curved edge and 1 vertex or apex. 

Triangular prism

This is a 3d figure, which has 2 triangular faces on either end and 3 rectangular faces. This 3D geometric shape has 5 faces, 9 edges, and 6 vertices. A triangular prism looks like a pyramid that has been stretched on both sides.

Square-based pyramid

This 3d figure is a pyramid with a square base and four triangular bases that are joined at a point called an apex or vertex. It has 5 faces, 8 edges and 5 vertices.

Help your child learn to identify different 3 dimensional geometric shapes with this 3D shapes worksheet.

Finding the Area of 2D and 3D Geometric Shapes

Area of 2D Geometric Figures

The area of a 2D shape is the space or region occupied by that shape. The area of a particular shape is measured in square units and is written as: cm² or m². In 2 dimensional shapes, the area of a 2D figure is the region enclosed within the boundary. Here is a table with the formulae to calculate the area of 2D shapes:

2d Geometric Shape Name	Calculating the Area	Area Formula
Circle	Area of a circle = π × Radius squared (Radius is the distance from the center of the circle to the circumference)	π × r2
Triangle	Area of a triangle = 1/2 x base (length of any one side of the triangle) x height (perpendicular distance from the base to the top vertex of the triangle)	1/2 x base x height
Square	Area of a square = S x S (S is the side or measure of the length and width of the square)	S2
Rectangle	Area of a rectangle = L x W (L is the length of the rectangle and W is the width of the rectangle)	L x W
Rhombus	Area of a rhombus = 1/2 x P x Q ( P and Q are the two diagonals of the rhombus)	1/2 x P x Q
Parallelogram	Area of a parallelogram = B x H (B is the base and H is the height, the vertical distance between the top and base of the parallelogram)	B x H

Area of 3D Geometric Figures

In a 3D object or shape, the total surface area (TSA) is the area of all the surfaces of the 3D object including the base. TSA is measured in square units and written as: cm² or m². Here is a table with the formulae to calculate the area of 3D shapes:

Shape	Calculating Total Surface Area	Total Surface Area Formula	Terms
Cube	Total Surface Area of a cube = sum of the areas of all the faces	6a2	a = length of the edge
Cylinder	Total Surface Area of a cylinder = sum of the area of the top and base and the area of the curved surface	2πr(r + h)	r = radius of circular baseh = height of the cylinder
Cone	Total Surface Area of a cone = sum of the area of the base and the curved surface area	πr(r + l)	r = radius of circular basel = slant height
Sphere	Total Surface Area of a sphere = 4 x π x radius squared	4πr2	r = radius of sphere
Cuboid	Total Surface Area of a cuboid = sum of areas of all 6 faces	2(lw+wh+lh)	l = lengthw = widthh = height

We hope you found this list of geometric shapes with their properties and classifications useful. For more exciting learning activities, games and worksheets, check our kids learning section.

Frequently Asked Questions on Geometric Shapes