Source: Safalta.comWe frequently see and interact with rectangular-shaped objects in our daily lives, including tables, books, boxes, mobile phones, walls, cricket fields, TV or computer screens, furniture, mattresses, almirahs, and doors. For a better understanding of the principles of the rectangle, we will explore the rectangle, its qualities, the area of a rectangle, formulas, the perimeter of a rectangle, and some solved problems based on it in this article. If you are preparing for competitive exams and looking for expert guidance, you can download our General Knowledge Free Ebook Download Now.
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Table of content
- Rectangle: Area
- Rectangle: Shape
- Rectangle: Area Formula
- Rectangle Area: Diagnol used
- Formula of rectangle
- Formula of Rectangle Perimeter
- Properties of rectangle
- Rectangle: Solved Examples
In the above figure, a rectangle ABCD is shown having sides in which the length of sides AB = CD = l, AD = BC = b, and AD || BC, AB || CD. The values of internal angles are 90°.
Area of rectangle = length × breadth
A = l × B Square units
Area of rectangle = length × breadth
A = l × b square units
- (Diagonal)2 = (Length)2 + (Width)2
- (Length)2 = (Diagonal)2 – (Width)2
- Length = √ (Diagonal)^2 – (Width)^2
- (Width)2 = (Diagonal)2 – (Length)2
- Width = √(Diagonal)^2 – (length)^2
- We know that the area of a rectangle is the product of length and breadth
- Area of rectangle = length × breadth
- Area of rectangle = length × √(Diagonal)^2 – (Length)^2
- or Area of rectangle = √ (Diagonal)^2 – (Width)^2 × width
A = L × W square units
Take into consideration the rectangle ABCD, which has the dimensions l and b. The perimeter of the rectangle ABCD is denoted by
The perimeter of the rectangle = 2 (l + b)
- An example of a quadrilateral is a rectangle.
- A rectangle's opposite sides are equal and parallel to one another.
- Each vertex of a rectangle has an internal angle of 90°.
- Rectangles' internal angles add up to 360° (90°+90°+90°+90°).
- A rectangle's diagonals cut each other in half.
- A rectangle's two diagonals are of equal length.
- The Pythagoras theorem can be used to determine the length of the diagonals. When the diagonal's sides are a and b, its length is equal to (a2 + b2).
- A rectangle is also referred to as a parallelogram since its sides are parallel.
- All parallelograms are absolutely rectangles, but not all rectangles are parallelograms.
1. If the length of a rectangle is 8cm and the breadth measures 5cm. Find the area of a rectangle.
Solution: Given l = 8cm and b = 5cm
then the area of rectangle A = l × b
A = 8 × 5
A = 40 sq. cm
2. The length and breadth of a rectangular courtyard are 75 m and 32 m.
Find the cost of leveling it at the rate of $3 per m2.
Also, find the distance covered by a boy to take 4 rounds of the courtyard.
Solution: Length of the courtyard = 75 m
The breadth of the courtyard = is 32 m
The perimeter of the courtyard = 2 (75 + 32) m
= 2 × 107 m
= 214 m
Distance covered by the boy in taking 4 rounds = perimeters of the courtyard
= 4 × 214
= 856 m
We know that the area of the courtyard = length × breadth
= 75 × 32 m22
= 2400 m22
For 1 m22, the cost of leveling = $3
For 2400 m22, the cost of leveling = $3 × 2400
3. Shyam has a rectangular photo frame that is 9 inches long and 5 inches wide. Help Shyam in finding the area of the photo frame.
Solution: We know the formula to calculate the area of a rectangle
Area of a Rectangle = (Length × Width).
Thus, the area of the rectangular frame = 9 × 5 = 45 square inches
Therefore, the area of the photo frame = 45 square inches
4. Find the perimeter and area of the rectangle o with a length of 17 cm and a breadth of 13 cm.
Solution: Given length = 17 cm, breadth = 13 cm
The perimeter of the rectangle = 2 (length + breadth)
= 2 (17 + 13) cm
= 2 × 30 cm
= 60 cm
We know that the area of the rectangle = length × breadth
= (17 × 13) cm2
= 221 cm2
5. A wire in the shape of a rectangle of length 35 cm and breadth of 18 cm is rebent to form a square. What will be the measure of each side?
Solution: The perimeter of the rectangle = 2 (35 + 18) cm
= 2 × 53
= 106 cm
The Perimeter of the square of side x cm = the, Therefore, the perimeter of the rectangle = Perimeter of the Square
106 cm = 4x
⇒ x = 26.5
Therefore, each side of the square = 26.5 cm
What are the 7 properties of rectangle?The fundamental properties of rectangles are:
- A rectangle is a quadrilateral.
- The opposite sides are parallel and equal to each other.
- Each interior angle is equal to 90 degrees.
- The sum of all the interior angles is equal to 360 degrees.
- The diagonals bisect each other.
- Both the diagonals have the same length.