## Geometric Shapes Definition

Geometric shapes are closed figures created using points, line segments, circles, and curves. Such shapes can be seen everywhere around us.

Some of the geometric shape examples are circle, rectangle, triangle, etc. A pizza is circular, whose slices are triangular. Similarly, doors and windows are examples of rectangles.

A regular shape has all sides equal. For example, a square or a regular hexagon. Irregular shapes have sides that are of different measures. For example, a scalene triangle.

Some of the most popular shapes are explained below:

- Rectangle

A rectangle is a shape that results from joining four different points through four different lines. In a rectangle, the opposite sides are parallel and equal in length. All the angles in a rectangle are right-angled. The difference between a rectangle and a square is that in a rectangle, two parallel line segments are longer than the other two, while in a square, all line segments are of equal length.

Examples of rectangular objects are laptop screens, mobile screens, etc.

- Square

A square is a four-sided geometric shape created by connecting four line segments of equal length. Similar to a rectangle, the line segments forming a square lie at right angles to each other. Examples of square objects are Rubik’s Cube, dice, chess boards, etc.

- Circle

A circle is a geometric shape made with no straight lines. We can assume that a circle is made of uncountable points placed at the same distance from the center point.

Examples of circular objects are whole pizzas and wheels.

- Triangle

A triangle is made up of three connected line segments. It is a complex geometric figure since it can have variable angles and measurements.

Examples of triangular objects are pizza slices, nachos, birthday caps, etc.

Notably, a triangle’s name changes depending on its angles and the size of the sides. For example, when two line segments of a triangle form a right angle, it is called a right triangle. Here’s how it looks:

Any triangle with angles less than 90 degrees is called an acute-angled triangle. Similarly, a triangle with one angle of more than 90 degrees is called an obtuse-angled triangle. An equiangular triangle has all interior angles equal to 60 degrees, and all the sides are equal in length. Refer to the diagram below to gain a better understanding.

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## Real-life Applications of Geometric Shapes

Geometry is the study of shape and space. It helps us understand other mathematical concepts as well as real-life applications. Geometry can be used for designing buildings, bridges, cars, and even clothes. The principles of geometry are also used in other branches of mathematics, such as trigonometry and calculus.

The following are some of the real-life applications:

Squares: Squares can be found in nature, for example, square-shaped crystals. Squares are also used in art. A famous painting by Piet Mondrian called “Composition with Red, Blue and Yellow” is a prime example.

Rectangles: Many man-made objects like TVs, books, and computer monitors are rectangular in shape. There are many real-life examples of rectangles, such as currency notes, cell phones, and book covers.

Circles: Circles can be seen everywhere around us, from the pizzas we eat to the face of a clock.

Triangles: You can find triangles in many places. Most roofs have triangular shapes called gables. Triangles can help support structures like bridges and buildings. There are even some chips that are shaped like triangles.

Ovals/Ellipses: An oval or ellipse is an elongated circle (egg-like in shape), where the length is greater than the width.

## Examples of three-dimensional shapes

Three-dimensional shapes are a group of vertices, lines that connect the vertices, and faces enclosed by these lines. They have length, breadth, and height and they occupy some volume. For many three-dimensional shapes, faces are two-dimensional. Also, some shapes in three dimensions have curved surfaces.

In three dimensions, the primary shapes are:

- Cube: Rubik’s Cube, Sugar cube
- Cone: Ice cream cone, Pyramid
- Cuboid: A wooden rectangular box, matchbox
- Cylinder: A toilet paper roll; a soda can
- Sphere: Football, Basketball

## Solved Examples

Example 1: How many sides does a decagon have?

Solution: A decagon has ten sides and ten vertices.

Example 2: What is a triangle with only two sides equal called?

Solution: A triangle with only two equal sides is called an isosceles triangle.

Example 3: Does a cone have a two-dimensional or three-dimensional form?

Solution: A cone is a three-dimensional figure.

## Practice Problems

## Geometric Shapes – Definition With Examples

### A square has _________.

A square, in geometry, is a plane figure that has four equal sides and four right angles.

The distance from the center of a circle to its outermost boundary is called the _________.

The distance from the center of a circle to its outermost boundary is called the radius of the circle. The diameter of a circle is always twice its radius.

### A cube is a _________.

A cube is a three-dimensional shape. It has six faces, eight vertices, and twelve edges. Each face of a cube is a square, and all the edges are of the same length. A cube has six square faces.

### An equilateral triangle is _________.

The sides of an equilateral triangle are of the same length. So, an equilateral triangle is a regular shape.

## Conclusion

Geometric shapes are part of our daily life. For learners, they help in laying the foundation of more complex concepts such as spatial relationships.

## Frequently Asked Questions

What are the basic geometric shapes?

The basic geometric shapes are circle, square, rectangle, triangle, etc. These shapes can further be arranged in varying combinations.

How are geometric shapes formed?

Geometric shapes are formed using lines, points, or curves. We should remember that these shapes need to fit a mathematical definition. If a shape cannot be mathematically defined, it is not geometric.

What are examples of shapes that are not geometric?

Shapes that are not geometric can be found in nature. For example, pebbles, rivers, etc.

How can we define a polygon?

A polygon is a shape made up of straight lines and no curves. It does not have any open sides. ‘Polygon’ is a broad term that represents different shapes, like squares, triangles, and rectangles.