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Area of Rectangle questions are an important part of quantitative aptitude section in various competitive exams The formula for area of rectangle is calculated by multiplying length and breadth.So the formula is: Area= Length X Breadth.Read this article to understand the concept of area of the rectangle .Not just the concept , we will try to make you understand the basics of the formula and how it is derived .This blog also contains some sample solved questions as well as advanced level questions on area of rectangle for your better understanding .
Table of Contents
What is a Rectangle?
A rectangle is classified as a quadrilateral, a two-dimensional shape with four sides.It’s important to differentiate between a rectangle and a square.
While a square represents a specific type of rectangle where all sides are of equal length, a rectangle can have varying length and width measurements as long as it maintains the properties of right angles and parallel sides.Two defining characteristics distinguish a rectangle:
- All four internal angles of the rectangle measure exactly 90 degrees (π/2 radians). This translates to each corner forming a perfect square where the sides meet.
- The opposing sides of the rectangle are both parallel and congruent (identical in length). This property bestows upon the shape a sense of balanced proportions.
Must Read:Area and Perimeter Questions with Answers
Area of Rectangle Formula
In simpler terms, the area of a rectangle is like the amount of flat space the rectangle fills. We find this area by multiplying the rectangle’s length by its width. Think of it like covering the rectangle with tiny squares: the more squares you can fit in a row (length) and the more rows you can fit (width), the greater the total area.
The symbol for area is typically capitalized “A,” and the length and width are represented by “l” and “b” (or sometimes “w”). So the formula we use to find the area looks like this: A = l × b. The answer will always be in square units, because we are essentially counting the number of tiny squares that fit within the rectangle.
Must Read:Find the Area of the Shaded Region: Square and Rectangle
Area of Rectangle : Sample Solved Questions
Q. A rectangular carpet has an area of 20 sq m. If the length is twice the breadth, what is the breadth?
a) 1 m
b) 2 m
c) 3 m
d) 4 m
Answer: b) 2 m (Let breadth = x. Then length = 2x. Area = 2x * x = 20. x^2 = 10. x = sqrt(10). Since width cannot be negative, x = 2)
Q. The diagonal of a rectangle divides it into two congruent right triangles. If the area of one triangle is 12 sq cm, what is the area of the rectangle?
a) 12 sq cm
b) 24 sq cm
c) 36 sq cm
d) 48 sq cm
Answer: c) 36 sq cm (Area of rectangle = 2 * Area of triangle = 2 * 12 = 24 sq cm)
Q. Tiles with a width of 10 cm are used to cover a rectangular floor. If 30 tiles are used in a row, what is the minimum possible length of the floor (in cm)?
a) 100
b) 200
c) 300
d) 400
Answer: b) 200 (Width of floor = Width of tile * Number of tiles = 10 * 30 = 300 cm. Since length cannot be smaller than width, minimum length = width = 300 cm)
Q. A rectangular park has a perimeter of 40 meters. If the length is 3 meters more than the breadth, what is the area of the park (in sq m)?
a) 54 sq m
b) 63 sq m
c) 72 sq m
d) 81 sq m
Answer: c) 72 sq m (Let breadth = x. Then length = x + 3. Perimeter = 2(x + x + 3) = 40. 4x = 34. x = 8.5. Area = (x + 3)x = (8.5 + 3)(8.5) = 72.25 ≈ 72 sq m)
Q. A rectangular sheet of paper is folded in half along its length. The resulting area is 18 sq cm. What is the original area of the paper?
a) 18 sq cm
b) 36 sq cm
c) 54 sq cm
d) 72 sq cm
Answer: b) 36 sq cm (The folded area represents half of the original sheet. Original area = Area of folded sheet * 2 = 18 * 2 = 36 sq cm)
Q. A rectangular garden is divided into two square plots. The total area of the garden is 48 sq m, and the area of one square plot is 16 sq m. What is the area of the other square plot (in sq m)?
a) 16 sq m
b) 24 sq m
c) 32 sq m
d) 48 sq m
Answer: a) 16 sq m (The garden consists of two identical squares. If one square plot has an area of 16 sq m, the other one must also have the same area)
Area of Rectangle : Questions (MCQ Format)
What is the formula for finding the area of a rectangle?
A) A = l + w
B) A = lw
C) A = 2(l + w)
D) A = 2lw
Answer: B) A = lw
If the length of a rectangle is 6 cm and the width is 4 cm, what is the area?
A) 24 cm
B) 20 cm²
C) 10 cm
D) 12 cm²
Answer: D) 12 cm²
A rectangle has an area of 35 square units and a width of 5 units. What is its length?
A) 5 units
B) 7 units
C) 10 units
D) 15 units
Answer: B) 7 units
If the area of a rectangle is 72 square meters and its length is 9 meters, what is its width?
A) 6 meters
B) 8 meters
C) 10 meters
D) 18 meters
Answer: A) 6 meters
What happens to the area of a rectangle if its length is doubled and its width remains the same?
A) It doubles
B) It triples
C) It quadruples
D) It remains the same
Answer: D) It remains the same
If a rectangle has a perimeter of 30 units and a length of 8 units, what is its width?
A) 5 units
B) 6 units
C) 7 units
D) 8 units
Answer: B) 6 units
The area of a rectangle is 45 square meters and its width is 9 meters. What is its length?
A) 4 meters
B) 5 meters
C) 6 meters
D) 7 meters
Answer: C) 6 meters
If the area of a rectangle is 60 square centimeters and its width is 6 centimeters, what is its length?
A) 9 centimeters
B) 10 centimeters
C) 11 centimeters
D) 12 centimeters
Answer: A) 9 centimeters
What is the area of a square with a side length of 10 meters?
A) 10 square meters
B) 20 square meters
C) 50 square meters
D) 100 square meters
Answer: D) 100 square meters
A rectangle has a length of 12 inches and a width of 5 inches. What is its area?
A) 17 sq inches
B) 45 sq inches
C) 60 sq inches
D) 72 sq inches
Answer: B) 60 sq inches
If a rectangle has a length of 20 meters and an area of 100 square meters, what is its width?
A) 2 meters
B) 3 meters
C) 4 meters
D) 5 meters
Answer: B) 5 meters
The area of a rectangle is 63 square units. If its width is 7 units, what is its length?
A) 9 units
B) 8 units
C) 10 units
D) 11 units
Answer: A) 9 units
If a rectangle has a width of 3 cm and an area of 24 cm², what is its length?
A) 8 cm
B) 9 cm
C) 10 cm
D) 12 cm
Answer: D) 12 cm
A rectangle has a perimeter of 24 cm and a width of 4 cm. What is its length?
A) 4 cm
B) 6 cm
C) 8 cm
D) 10 cm
Answer: B) 6 cm
If a rectangle has a length of 15 units and an area of 75 square units, what is its width?
A) 3 units
B) 4 units
C) 5 units
D) 6 units
Answer: C) 5 units
What is the area of a rectangle if its length is 16 meters and its width is 8 meters?
A) 64 square meters
B) 100 square meters
C) 128 square meters
D) 144 square meters
Answer: A) 64 square meters
If a rectangle has a length of 18 inches and an area of 90 square inches, what is its width?
A) 3 inches
B) 4 inches
C) 5 inches
D) 6 inches
Answer: A) 5 inches
A rectangle has a length of 9 cm and a width of 6 cm. What is its area?
A) 15 cm²
B) 36 cm²
C) 45 cm²
D) 54 cm²
Answer: D) 54 cm²
The area of a rectangle is 48 square units. If its width is 6 units, what is its length?
A) 6 units
B) 7 units
C) 8 units
D) 9 units
Answer: C) 8 units
If the length of a rectangle is 5 units and the width is 3 units, what is its area?
A) 8 units
B) 15 units
C) 10 units
D) 7 units
Answer: B) 15 units
A rectangle has a length of 12 cm and a width of 8 cm. What is its area?
A) 20 cm²
B) 80 cm²
C) 96 cm²
D) 64 cm²
Answer: D) 64 cm²
If the area of a rectangle is 45 square meters and its width is 5 meters, what is its length?
A) 9 meters
B) 8 meters
C) 7 meters
D) 6 meters
Answer: A) 9 meters
What happens to the area of a rectangle if its length is doubled while keeping the width constant?
A) It doubles
B) It halves
C) It triples
D) It remains the same
Answer: A) It doubles
If the area of a rectangle is 72 square units and its width is 6 units, what is its length?
A) 12 units
B) 16 units
C) 14 units
D) 10 units
Answer: A) 12 units
The length of a rectangle is 20 cm and its area is 180 cm². What is its width?
A) 6 cm
B) 9 cm
C) 8 cm
D) 7 cm
Answer: B) 9 cm
If the length of a rectangle is x + 4 and its width is x – 2, what is its area in terms of x?
A) x² – 8
B) x² + 2x – 8
C) x² + 2x + 8
D) x² – 4
Answer: B) x² + 2x – 8
The perimeter of a rectangle is 30 cm and its length is 10 cm. What is its area?
A) 50 cm²
B) 60 cm²
C) 70 cm²
D) 80 cm²
Answer: A) 50 cm²
If the area of a rectangle is 100 square units and its length is 10 units, what is its width?
A) 5 units
B) 10 units
C) 15 units
D) 20 units
Answer: A) 5 units
A rectangle has a length twice its width. If its perimeter is 24 units, what is its area?
A) 12 square units
B) 24 square units
C) 36 square units
D) 48 square units
Answer: C) 36 square units
The length of a rectangle is 3 more than its width. If its perimeter is 30 cm, what is its area?
A) 36 cm²
B) 45 cm²
C) 54 cm²
D) 63 cm²
Answer: A) 36 cm²
A rectangle has a length of 8 meters and a width of 6 meters. What is its perimeter?
A) 20 meters
B) 28 meters
C) 32 meters
D) 48 meters
Answer: B) 28 meters
If the length of a rectangle is halved and its width is tripled, what is the change in its area?
A) Decreased by 50%
B) Increased by 50%
C) Increased by 100%
D) Decreased by 75%
Answer: D) Decreased by 75%
The perimeter of a rectangle is 50 cm and its length is 15 cm. What is its width?
A) 10 cm
B) 12 cm
C) 5 cm
D) 8 cm
Answer: D) 8 cm
A rectangle has a length of 14 units and a width of x units. If its area is 168 square units, what is the value of x?
A) 6 units
B) 8 units
C) 10 units
D) 12 units
Answer: A) 6 units
If the length of a rectangle is doubled and its width is halved, what happens to its area?
A) It doubles
B) It quadruples
C) It halves
D) It remains the same
Answer: D) It remains the same
The area of a rectangle is 48 square meters. If its length is 12 meters, what is its width?
A) 2 meters
B) 3 meters
C) 4 meters
D) 6 meters
Answer: C) 4 meters
A rectangle has a width of 10 units and an area of 80 square units. What is its length?
A) 4 units
B) 6 units
C) 8 units
D) 12 units
Answer: B) 6 units
If the length of a rectangle is one-third of its width and its perimeter is 24 units, what is its area?
A) 8 square units
B) 12 square units
C) 16 square units
D) 24 square units
Answer: B) 12 square units
FAQs
To find the area of a rectangle problem ,multiply length by width to get the area.
In this case,divide area by length to find breadth.so breadth is 17 cm.
Area formula for rectangles is : Area = Length × Width
To solve rectangle problems: Identify length and width, then apply area formula: Length × Width.
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