Area Of Shapes

An area is a quantity that expresses the extent of a two-dimensional figure or shape or planar lamina in the plane.

Lamina shapes include 2D figures that can be drawn on a plane, for e.g., circle, square, triangle, rectangle, trapezium, rhombus and parallelogram.

Polygon shape

A polygon is a two-dimensional shape that is formed by straight lines. The examples of polygons are triangles, hexagons and pentagons. The names of shapes describe how many sides exists in the shape. For instance, a triangle consists of three sides and rectangle has four sides. Hence, any shape that can be formed using  three straight line is known as a triangle and any shape that can be drawn by linking four lines is known as quadrilateral.

The area is the region inside the boundary/perimeter of the shapes which is to be considered.

In general, the area of shapes can be defined as the amount of paint required to cover the surface with a single coat. Following are the ways to calculate area based on number of sides that exist in the shape, as illustrated below in Fig.

Mathematical Shapes

Area Of Shapes

According to International System of Units (SI), the standard unit of area is the square meter (written as m2) and is the area of a square whose sides are one meter long. For example, a particular shape with an area of three square meters would have the same area as three such squares

For 3D/ solid shapes like cube, cuboid, sphere, cylinder and cone, the area is updated to the concept of surface area of the shapes.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

In addition to the area of the planar shapes an additional variable i.e the height or the radius are taken into account for computing the surface area of the shapes.

Area Of Shapes

The above concepts are very well illustrated in the Byju’s videos. For instance, consider finding the area of the circle as  πr² by the following method:

Consider a circle of radius r and make endless concentric circles. Now from the center to the boundary make a line segment equal to the radius and cut the figure along with that segment.

It’ll be formed a triangle with base equal to the circumference of the circle and height is equal to the radius of the outer circle, i.e., r. The area can thus be calculated as ½ * base * height  i.e

½ * 2πr*r

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Practise This Question

Find the least fraction, which must be multiplied to (124 12 +3616 116 +28) to make it an integer.