Area of shapes such as circle, triangle, square, rectangle, parallelogram, etc. are the region occupied by them in space. 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, 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 exist in the shape. For instance, a triangle consists of three sides and a rectangle has four sides. Hence, any shape that can be formed using three straight lines is known as a triangle and any shape that can be drawn by linking four lines is known as a quadrilateral. The area is the region inside the boundary/perimeter of the shapes which is to be considered.
Here in this article, we have discussed the area formula for all the different types of shapes introduced in Maths and along with that solved some problems based on those formulae.
Area of Different Shapes Formula
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 the number of sides that exist in the shape, as illustrated below in Fig.
Let us write the formulas for all the different types of shapes in a tabular form.
|Circle||π × r2||r = radius of the circle|
|Triangle||½ × b × h||b = base
h = height
|Square||a2||a = length of side|
|Rectangle||l × w||l = length
w = width
|Parallelogram||b × h||b=base
|Trapezium||½(a+b) × h||a and b are the length of parallel sides
h = height
|Ellipse||πab||a = ½ minor axis
b = ½ major axis
Area of Solid Shapes in Maths
According to the 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. The surface area of a solid object is a measure of the total area that the surface of the object occupies.
For 3D/ solid shapes like cube, cuboid, sphere, cylinder and cone, the area is updated to the concept of the surface area of the shapes. The formulas for three-dimension shapes are given in the table here:
|Cube||a2||a = length of the edge|
|Rectangular Prism||l x b x h||l=length
|Cylinder||πr2h||r = radius of circular base
h= height of cylinder
|Cone||⅓ π r2h||r = radius of circular base
h= height of cone
|Sphere||4/3 π r2||r = radius of sphere|
|Hemi-sphere||2/3π r2||r = radius of sphere|
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.
Consider a circle of radius r and make endless concentric circles. Now from the centre 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
Q,1: Find the area of the circular path whose radius is 7m.
Solution: Given, radius of circular path, r = 7m
By the formula of area of circle, we know;
A = π r2
A = 22/7 x 7 x 7
A = 154 sq.m.
Q.2: The side-length of a square plot is 5m. Find the area of a square plot.
Solution: Given, side length, a = 5m
By the formula of area of a square, we know;
Area = a2
A = 5 x 5
A = 25 sq.m.
Q.3: Find the area of the cone, whose radius is 4cm and height is 3cm.
Solution: Given, radius of cone = 4cm
and height of cone = 3cm.
As per the formula of area of cone, we know;
Area = 1/3 π r2h
A = 1/3 x 22/7 x 4 x 4 x 3
A = 22/7 x 4 x 4
A = 50.28 sq.cm.