How to Calculate Area of Common 2D Shapes Efficiently
In Geometry, a shape is defined as a figure that is enclosed by a boundary. The border of the shapes is formed by lines, points, and curves. Two-dimensional (2D) shapes are bordered by straight lines. The 2D shapes have only length and breadth and they are popularly known as polygons and flat shapes. These include squares, rectangles, circles, rhombuses, and triangles. The area of a 2D shape is the region enclosed within the boundary which is measured in square units. Now, we will discuss more details about basic 2-dimensional shapes and their Areas.
Area of a Rectangle
The area of a rectangle in a two-dimensional region is the area covered by the rectangle. A rectangle is a two-dimensional form with four sides and four vertices. All the four angles in a rectangle are 90 degrees. The opposite sides of the rectangle are equal and parallel to one another.
Formula: Area of a rectangle = Length (L) x Breadth (W) (or width)
The shaded region represents the area of a rectangle with length and width
Example: Find the area of a rectangle with a length of 4 metres and a width of 2 metres.
Ans: Given length L = 4 m and width (W) = 2m
Area of the given rectangle = 4 x 2 = 8 sq.m
Area of a Square
A Square is a 2-Dimensional shape just like a rectangle. The only difference between a square and a rectangle is that in a rectangle only opposite sides are equal whereas in a square shape, all sides are equal. We can say a square is a rectangle with all of its sides being the same length.
Formula: Area of a square = side x side = (side)2
The shaded region represents the area of a square
Example: Find the area of a square whose side measures 3 cm.
Ans: Given the side of a square = 3cm
So, the area of the square = 3 x 3 = 9 sq.cm.
Area of a Circle
A circle is a closed curve with an exterior line that is equidistant from the centre. The radius of the circle is the fixed distance from the centre point to the boundary of the circle. Many examples of the circle can be found in everyday life, such as a wheel, pizzas, a round ground, and so on.
Formula: Area of circle with radius ‘r’ is given by the formula A = πr2
Shaded region represents the area of a circle with radius r.
Example: Find the area of a circle whose radius is 5 metres.
Ans: Given, radius of the circle r = 5m
Therefore, area of the circle = π(5)2= π(25) = 25 square units
Area of a Triangle
A triangle is one of the most fundamental 2-Dimensional shapes with three sides and three vertices. The area of the triangle is the region occupied inside the boundary of the triangle.
Formula: Area of a triangle with base ‘b’ and height ‘h’ = 1/2 base x height
The shaded region represents the area of a triangle with base (b) and height (h).
Example: Find the area of the triangle with height 4m and base 3m.
Ans: Given, the height of the triangle (h) = 4m
The base of the triangle (b) = 3m
Area of the triangle = $\frac{1}{2}$ x 4 x 3 = 6 sq.m
Area of an Equilateral Triangle
An equilateral triangle is a type of triangle in which all sides are equal in length.
Formula: Area of an equilateral triangle = $\frac{\sqrt{3}}{4}$ x side2
The shaded region in the above image shows the area of an equilateral triangle with side ‘a’.
Example: Find the area of an equilateral triangle with side length equal to 2m.
Ans: Given the side of an equilateral triangle is 2m.
So, the area of the given equilateral triangle is = $\frac{\sqrt{3}}{4}$ x (2)2 = $\sqrt{3}$ sq. m
Area of a Parallelogram
A parallelogram is a quadrilateral, in which opposite sides are equal in length and parallel but the angles are not equal to 90 degrees.
Formula: The area of a parallelogram with base ‘b’ and height ‘h’ is
A = base (b) x height (h)
The shaded region shows the area of a parallelogram
Example: Find the area of a parallelogram with a base length of 9m and height of 3m.
Ans: Given, parallelogram has base length b = 9m and height h = 3m.
So, the area of the given parallelogram is A = 3 x 9 = 27 sq.m
Areas of 2D Shapes Chart
The below chart shows various two-dimensional shapes with their corresponding formulas which can be kept handy to refer to in future.
The above table shows 2D shapes and their corresponding areas.
Conclusion
In Mathematics, 2D shapes are planar figures that can be drawn on a flat surface or a sheet of paper. Two-dimensional shapes have sides and corners, while others have curved boundaries. The area of a 2-D shape is the region enclosed within the boundary of the shape. Learning 2D shapes and their areas is fun and helps the kids to improve their geometry skills.
FAQs on Area of 2D Shapes: Definitions, Formulas & Real-Life Examples
1. What are 2D shapes? Give some common examples.
2D shapes, or two-dimensional shapes, are flat figures that have only two dimensions: length and width. They do not have any thickness or depth, meaning you can draw them on a piece of paper, but you cannot hold them in your hand. Common examples of 2D shapes include circles, squares, rectangles, triangles, and pentagons.
2. What are the basic properties used to describe 2D shapes?
The basic properties used to describe 2D shapes, especially polygons, are:
Sides: These are the straight line segments that make up the boundary of a shape.
Vertices (or Corners): A vertex is a point where two sides meet.
Angles: An angle is formed at a vertex, inside the shape.
For example, a triangle has 3 sides, 3 vertices, and 3 angles. A circle is a special case with one curved side and no vertices.
3. How are 2D shapes different from 3D shapes?
The main difference between 2D and 3D shapes is the number of dimensions they have. 2D shapes are flat and have only two dimensions (length and width). In contrast, 3D shapes are solid and have three dimensions: length, width, and depth (or height). You can measure the area and perimeter of a 2D shape, while you can measure the volume and surface area of a 3D shape. A square is a 2D shape, while a cube is its 3D counterpart.
4. What are some real-life examples of 2D shapes we see every day?
We are surrounded by objects that represent 2D shapes. For example:
A circle can be seen in a wall clock, a plate, or a car's steering wheel.
A square can be seen on a chess board, a slice of bread, or a wall tile.
A rectangle is visible in a door, a smartphone screen, or a book cover.
A triangle can be found in a slice of pizza, a traffic sign, or a clothes hanger.
5. What is the difference between the area and perimeter of a 2D shape?
The perimeter and area are two distinct measurements of a 2D shape. The perimeter is the total distance around the boundary of the shape; it is a measure of length (e.g., in cm, m). The area, on the other hand, is the amount of surface or space enclosed within the boundary of the shape; it is measured in square units (e.g., in cm², m²).
6. What are the formulas for the area of common 2D shapes?
The formula for calculating the area varies for each shape:
Square: Area = Side × Side
Rectangle: Area = Length × Width
Triangle: Area = ½ × Base × Height
Circle: Area = π × radius² (where π is approximately 3.14 or 22/7)
7. Can a circle be considered a polygon? Why or why not?
No, a circle cannot be considered a polygon. A key characteristic of a polygon is that it must be made up of straight line segments. A circle, by definition, is a curved line where all points on the line are equidistant from a central point. Since it does not have straight sides or vertices, it does not meet the criteria to be classified as a polygon.
8. Why is it important to learn about 2D shapes?
Learning about 2D shapes is a fundamental part of mathematics and has many practical applications. It helps develop spatial reasoning and problem-solving skills. Understanding shapes is crucial in fields like art, architecture, engineering, and design. For example, an architect uses knowledge of rectangles and triangles to design a stable building, and an artist uses circles and ovals to draw realistic figures.
