Area and perimeter are two basic measurements used to describe two-dimensional shapes. The perimeter is the total distance around the boundary of a shape, while the area tells us how much surface the shape covers inside its boundary.
In the image, the area is the green region inside the fence, and the perimeter is the total length of the fence around the garden.
Area: Area is the amount of space covered inside a closed two-dimensional shape. It tells us how much surface is inside the boundary and is measured in square units (like m² and cm²).
Perimeter: Perimeter is the total distance around the boundary of a closed two-dimensional shape. It is measured in units like meters or centimeters.
The 2D shapes have some specific properties related to their dimensions and the orientation of their dimensions, which they adhere to. Every shape has defined formulae to calculate its area and perimeter.
Triangle
A triangle is a closed figure having three sides. It has three vertices. The altitude, or height, of a triangle is the perpendicular drawn from one of its vertices to meet the opposite side.
The side to which the perpendicular meets is called the base of a triangle.
- Area of a triangle = 1/2 × (base) × (height)
- Perimeter of a triangle = Sum of all three sides
Rectangle
A rectangle is a four-sided polygon having opposite sides equal and parallel. All the angles of a rectangle are equal to 90°.
The longer side of a rectangle is known as the length of the rectangle, and the other side is called the breadth or width of the rectangle.
- Area of a rectangle = length × breadth
- Perimeter of a rectangle = 2 × (length + breadth)
Square
A square is a four-sided polygon having all four sides equal and parallel to each other. Also, all angles of a square have a measure of 90° each. Thus, a square can be said to be a special type of rectangle having all four sides equal.
- Area of a Square = (side) × (side)
- Perimeter of a Square = 4 × (side)
Parallelogram
A parallelogram is a four-sided polygon having opposite sides equal and parallel. The perpendicular distance between two opposite sides is called the height of a parallelogram. The length of those sides is called the base of a parallelogram.
- Area of a Parallelogram = Base × Height
- Perimeter of a Parallelogram = 2 × (Sum of opposite sides)
Rhombus
A rhombus is a four-sided polygon having all four sides equal and opposite sides being parallel to each other. The area of a rhombus is calculated by the measure of the length of its diagonals.
- Area of a Rhombus = 1/2 × ( Product of diagonals)
- Perimeter of a Rhombus = 4 × side
Trapezium
A trapezium is a four-sided polygon having two opposite sides parallel to each other. The other two sides may or may not be parallel. The distance between two parallel sides is known as the height of the trapezium.
- Area of a trapezium = 1/2 × (Sum of parallel sides) × (height)
- Perimeter of a trapezium = (Sum of all 4 sides)
Circle
A circle is a round-shaped figure in which the distance of all points lying on it from its center is equal. This distance is called the radius of the circle. The perimeter of a circle is known as its circumference.
Area of a Circle = πr2
Perimeter of a Circle = 2πr
Semicircle
A semicircle is half of a circle whose one side is curved and other side is bounded by the diameter of the circle.
- Area of Semicircle = 1/2 × π × r2
- Perimeter of Semicircle = πr + 2r
Area and Perimeter Formulas
Area vs Perimeter
The differences between area and perimeter are listed in form of a table below:
Area | Perimeter |
|---|---|
Area is a measure of a region's size on a surface. The region is a closed 2D figure. | Perimeter is a measure of the length of boundary of any closed 2D shape. |
Area is expressed in square units, such as m2, cm2, mm2, etc. | It is expressed in units, such as m, cm, mm, etc. |
Example: The space occupied by a park. | Example: The length of the boundary of the park. |
Also Check:
Solved Examples
Example 1: Find the values of perimeter and area for rectangular park having length as 40 m and the breadth as 50 m.
Solution:
Given:
Length of rectangle, l = 40 m
Breadth of rectangle, b = 50 mWe know that,
Perimeter of rectangle = 2(l + b)
= 2(40 + 50)
= 2 × 90
= 180 mArea of rectangle = l × b
= 40 × 50
= 2000 m²Thus, the perimeter of the rectangle is 180 m and the area is 2000 m².
Example 2: A circular running track has a radius of 7 meters. Find its circumference. Take π = 22/7.
Solution:
We have,
Radius of the circle, r = 7 mCircumference of a circle = 2πr
Therefore,
Circumference = 2 × (22/7) × 7
= 44 mThus, the circumference of the circular track is 44 meters.
Example 3: The opposite sides of a parallelogram have values of 12 units and 8 units. Find the value of its perimeter.
Solution:
We know that,
Perimeter of a parallelogram = 2 × (sum of adjacent sides)Thus,
Perimeter = 2 × (12 + 8) = 2 × 20 = 40 units
Practice Questions on Area and Perimeter
Following are some practice questions based on calculating area and perimeter for you to solve.
Q1. Find the area of a trapezium whose parallel sides measure 12 cm and 14 cm. The distance between parallel sides is equal to 6 cm.
Q2. Calculate the perimeter of a regular pentagon having each side equal to 5 inches.
Q3. A circle has a diameter of 14 cm. Find the values of its circumference and area. Use π = 22/7.
Q4. The perimeter of a circle is 44 m. Find its radius and then calculate its area.