Area refers to the amount of space inside a shape or surface. The area of a shape can be determined by placing the shape over the grid and counting the number of squares that itcovers. Various shapes have various formulas to calculate the area, known as area formulas.
Area formulas are essential tools used in mathematics to calculate the amount of space enclosed by different two-dimensional shapes. These formulas can be used to find the area of geometric figures such as squares, rectangles, circles, triangles, trapezoids, and ellipses.
Given below is the different area formulas chart for various 2d shapes.
Area is measured in square units. The SI unit to measure the area is m2.
Here we will learn about various area formulas for 2d shapes as well as 3d shapes along with their solved examples.
Table of Content
Area Formulas of 2D Shapes
Shapes that have only two dimensions are called 2-D shapes. They are drawn in 2-D space and are dependent on 2 parameters, generally length(l) and breadth(b). The various 2-D shapes are Rectangle, Square, Triangle, Circle, and others.
Area of 2D shapes formulas are the formulas that are used to find the area of various 2D shapes, such as the area of a triangle, area of a square, area of a rectangle, area of a rhombus, etc. These area formulas are highly used in mathematics to solve various geometrical problems. Various area formulas for various shapes are,
Area Formula of a Rectangle
It is a 2-dimensional figure which is a quadrilateral, i.e., it has four sides; its opposite sides are parallel and equal. All the angles in the rectangle are equal and their measure is 90 degrees. The diagonals of the rectangle are equal and they are perpendicular bisectors of each other.
The formula for calculating the area of a rectangle is length l and breadth b is,
- Area of Rectangle (A) = l×b square units
Area Formula of a Square
is a 2-dimensional figure which is a quadrilateral, i.e., it has four sides; its opposite sides are parallel, and all four sides in a square are equal. All the angles in the square are equal and their measure is 90 degrees. The diagonals of the square are equal, and they are perpendicular bisectors of each other.
The formula for calculating the area of a square with side a is,
- Area of Square (A) = a2 sq. units
Area Formula of a Triangle
A triangle is the simplest polygon that is made by joining three straight lines. The sum of the lengths of all sides of the triangle is the perimeter of the triangle, and the space inside the perimeter of the triangle is the area of the triangle.
The formula for calculating the area of a triangle with base b and height h is,
- Area of Triangle (A) = 1/2 × bh sq. units
Area Formula of a Circle
Circleis a geometrical figure with no straight lines. It is the locus of the point that is always at a constant distance from the fixed point. The fixed point is called the center of the circle, and the fixed distance is the radius of the circle.
The formula for calculating the area of a circle with r as the radius of the circle is,
- Area of Circle (A) = πr2 sq. units
Area Formula of a Parallelogram
A Parallelogram is a 2-D figure in which the opposite sides are parallel and equal. The formula for calculating the area of a parallelogram with base b and height h is,
- Area of Parallelogram (A) = bh sq. units
Area Formula of a Rhombus
A Rhombus is a quadrilateral with all four sides equal and parallel, but not all angles are equal. The formula for calculating the area of a rhombus with diagonals d1 and d2,
- Area of Rhombus (A) = 1/2 × d1 × d2 sq. units
Area Formula of a Trapezoid
Trapezoid is another name of trapezium. It is a quadrilateral in which the opposite sides are parallel. The formula for calculating the area of a trapezoid with parallel sides a and b and height h is,
- Area of Trapezoid (A) = 1/2(a +b)h sq. units
Area Formula of an Ellipse
An Ellipse is a 2-D shape and comes under conic sections. The formula for calculating the area of an ellipse with axes a and b,
- Area of Ellipse (A) = πab sq. units
Area Formula of a Semicircle
A Semicircle is a 2-D figure that is half of a circle. The formula to calculate the area of a semicircle with radius r is,
- Area of Semicircle (A) = 1/4(πr2) sq. units
Area Formulas Table
The formulas for the areas of the various 2-D figures are added in the table below.
Area of Shape | Area Formula | Variables |
|---|---|---|
Area of a Rectangle | Area = l × b |
|
Area of Square | Area = a 2 | a is the side of the square |
Area of Triangle | Area = 1/2 × bh |
|
Area of Circle | Area = πr2 | r is the radius of the circle |
Area of Trapezoid | Area = 1/2 × (a+b)h |
|
Area of Rhombus | Area = 1/2 × d1 × d2 |
|
Area of Parallelogram | Area = b × h |
|
Area of Ellipse | Area = πab |
|
Area of 3D Shapes Formula
3-D shapes are the shapes that are drawn in 3-D spaces. They have 3 dimensions that are their parameters. The area of these shapes is dependent on the length, breadth, and height of 3-D shapes. Various 3-D shapes are Cube, Cuboid, Cylinder, Cone, Sphere, and others.
The area of 3-D shapes is of two categories that are
- Curved Surface Area (Lateral Surface Area){CSA}, and
- Total Surface Area(TSA).
The CSA is the area of all the curved surface of the 3-D shapes and TSA is the area of all the faces of the 3-D shapes.
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Area of the 3-D shapes are the space occupied by all the faces of the figure. It is measured in units2. The SI unit of area is m2. The area of cube, area of cuboid, area of cylinder, area of cone, and others a in the area of 3D shapes. The table added below shows the formulas of various 3-D figures.
Area of Shape | Surface Area | Parameters |
|---|---|---|
6a2 | a is the Length of the Edge | |
2(lb + lh + bh) |
| |
πr(r + l) |
| |
2πr(r + h) |
| |
4πr2 | r is the Radius of the sphere | |
3πr2 | r is the Radius of the hemisphere | |
2(wl + hl + hw) |
|
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Solved Examples of Area Formulas
Example 1: Find the area of a rectangle with a length of 5 cm and a breadth of 2 cm.
Solution:
Given,
- Length of the Rectangle (l) = 5 cm
- Breadth of the rectangle (b) = 2 cm
Area of Rectangle(A) = l × b
A = 5cm × 2cm
= 10cm2
Example 2: Find the area of the square park whose side is 4 m.
Solution:
Given,
Side of Square (a) = 4 m
Area of Square = a2
= (4)2 = 16 m2Thus, the area of the square park is 16 m2
Example 3: Find the area of a triangular plate whose height is 6 cm and the base is 6 cm.
Solution:
Given,
Height of Triangle (h) = 6 cm
Base of Triangle (b) = 8 cmArea of Triangle(A) = 1/2(b × h)
A = 1/2(8 × 6)
= 48/2 = 24 cm2The area of the triangular plate is 24 cm2
Example 4: Find the area of a circular disc with a radius of 1.4 cm.
Solution:
Given,
Radius of Circle (r) = 1.4 cm
Area of Circle(A) = πr2A = π(1.4)2
= 22/7(1.4)(1.4) = (4.4)(1.4)
= 6.16 cm2The area of the circular disc is 6.16 cm2
Conclusion
Area formulas allow us to accurately calculate the amount of space enclosed by different geometric figures, such as rectangles, squares, circles, and more complex shapes like cubes and spheres. Mastery of these formulas is essential for solving mathematical problems and is widely utilized in fields such as engineering, architecture, and design. By using these area formulas, one can efficiently determine areas for practical applications, ranging from calculating the space of a room to designing architectural structures.