What is the Definition of Area?
The area of a two-dimensional shape is the amount of space it covers within its boundary. To state this in an alternative manner, it’s the number of unit squares that cover the surface of a closed two-dimensional figure. Square units, which are commonly represented as square inches, square feet, and so on, are the standard units that we use to represent the area of a closed shape.
What is a Rectangle?
In geometry, a rectangle is a two dimensional shape with four sides and four corners, or vertices. Two of its sides are at a right angle to each other. As a result, a rectangle has four angles, each measuring 90 degrees. The lengths of the opposite sides of a rectangle are also equal and parallel.
The rectangle, the most common shape, is a part of our daily life. Real-world examples of rectangles include laptops, books, cell phones and TVs.
Properties of Rectangles
Rectangles have the following basic properties:
1) The four internal angles are all 90 degrees.
2) The opposite sides are parallel and equal.
3) A rectangle is surely a quadrilateral.
4) The perimeter of a rectangle with side lengths “a” and “b” is “2a + 2b” units.
Formulas Related to a Rectangle
There are three main formulas that are related to a rectangle that must be remembered. They help us with obtaining the area and the perimeter of a rectangle.
Area of a rectangle: A = \(l\times w\), where “l” and “w” are the length and width of a rectangle, respectively.
Solved Examples
Example 1:
Find the area of a rectangle with the given dimensions.
Solution:
Step 1: Find a smaller rectangle with unit fraction side lengths using the denominators of the side lengths.
Step 2: Calculate the area of the rectangle with sides of \( \frac{1}{5} \) and \( \frac{1}{2} \) inches.
There are 5 × 2 = 10 of these rectangles in a square unit, so each area is \( \frac{1}{10} \) square unit.
Step-3: Find the area of the large rectangle.
It takes 2 × 3 = 6 of the smaller rectangles to fill the large rectangle. So, the area of the large rectangle is \(6\times \frac{1}{10}=\frac{6}{10}\), or 0.6 square units.
Example 2:
Calculate the area of a rectangle whose length and width are 14 cm and 10 cm, respectively.
Solution:
The properties of a rectangle can be used to calculate the area of a rectangle. The length of the given rectangle is 14 cm, and its width is 10 cm.
We know that the area of a rectangle can be calculated by its length multiplied by its width.
Therefore,
Area of the rectangle = length x width
Area of the rectangle = 14 x 10 = 140 cm²
Example 3:
A rectangular wall’s length and width are 40 m and 25 m, respectively. Calculate the cost of painting the wall at a rate of 5 dollars per sq. m.
Solution:
Length of the wall = 40 m
Width of the wall = 25 m
Area of the wall = length × breadth = 40 m × 25 m = 1000 sq.m.
Since painting 1 sq. m. costs 5 dollars
Hence, for 1000 sq. m., the cost of painting the wall will be
= 5×1000 = 5000 dollars
Example 4:
A rectangular screen measures 15 inches in length. It has a surface area of 225 square inches. Find out how wide it is.
Solution:
Area of the screen = 225 square inches.
Length of the screen = 15 in
Area of a rectangle = length x width
So, width = \( \frac{\text{area}}{\text{length}} \)
Thus, width of the screen = \(\frac{225}{15}\) = 15 in
Yes, a square is considered a rectangle because it has all of the properties of a rectangle, such as all four interior angles being 90 degrees, opposite sides being parallel and equal, and two diagonals being equal and that bisect each other.
A rectangle is a two-dimensional shape that has four sides, four angles, and four vertices. The opposite sides are equal and parallel to one another in a rectangle. Additionally, the interior angles are equal and measure 90 degrees each.
The region occupied by the rectangle’s sides is known as the rectangle’s area.
Any shape’s area is measured in square units. For instance, sq.m. or \(m^2\).