MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
Addition, Multiplication, Division
4 Grade
Adding and Subtracting
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Polynomial Vocabulary
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Linear Functions
8 Grade
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Extremal value problems
Trigonometry
Numbers Classification
Geometry
Slope
Intercept Theorem
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Home
Practice
Area of Squares and Rectangles
Area of Squares and Rectangles: Problems with Solutions
By Catalin David
Problem 1
A rectangle has a length of 6 inches and a width of 4 inches. The area is
in
^{2}
Solution:
Area of a rectangle is L × W where L is the length and W is the width
6 × 4 = 24 in
^{2}
.
Problem 2
The side of a square is 5 meters. The area of the square is
m
^{2}
Solution:
The sides of а square are equal size. The square's area is a × a where
a
is the side of the square.
5 × 5 = 25
Problem 3
The area of a square is 16 in
^{2}
. Its side is
in.
Solution:
Area = a × a where
a
is the length of a side
a × a = 16
4 × 4 = 16
a = 4
Problem 4
The area of a rectangle is 45 cm
^{2}
. If its length is 9 cm, then its width is
cm
Solution:
Area = L × W
45 = 9 × W
W = 45 ÷ 9 = 5
Problem 5
The perimeter of a square is 24 cm. The area of the square is
cm
^{2}
Solution:
Perimeter is 4 × a where
a
is the side of the square
4 × a =24
a = 24 ÷ 4 = 6
Area = a × a = 6 × 6 = 36 cm
^{2}
Problem 6
The length of a rectangle is 12 cm and its width is 5 cm smaller. The area of the rectangle is
cm
^{2}
.
Solution:
L = 12
W = 12 - 5 = 7
Area = L × W = 12 × 7 = 84 cm
^{2}
Problem 7
A rectangle has the length of 12 cm and the width 3 times smaller. Its area is
cm
^{2}
Solution:
L = 12
W = 12 ÷ 3 = 4
Area = L × W = 12 × 4 = 48 cm
^{2}
Problem 8
The length of a rectangle is 6 cm and the width is 4 cm. If the length is greater by 2 cm, what should the width be so that the new rectangle have the same area as the first one?
Solution:
The area of the first rectangle is L × W = 6 × 4 = 24 cm
^{2}
The new length is 6 + 2 = 8 cm
8 × W = 24 then W = 24 ÷ 8 = 3 cm
Problem 9
How many squares with the side of 2 cm cover the surface of a rectangle with a length of 24 cm and a width of 8 cm?
Solution:
The area of the square is 2 × 2 = 4 cm
^{2}
The area of the rectangle is L × W = 24 × 8 = 192 cm
^{2}
The number of squares is 192 ÷ 4 = 48
Problem 10
A square with a side of 6 cm and a rectangle with a width of 4 cm have the same area. What's the length of the rectangle?
Solution:
The area of the square is 6 × 6 =36 cm
^{2}
The area of the rectangle is L × W. Because the areas are equal L × W = 36
L × 4 = 36
L = 36 ÷ 4 = 9 cm
Problem 11
The side of a square is 5 cm. If its side is doubled, how many times is the area of the new square bigger than the area of the old square?
Answer:
times.
Solution:
The area of the first square is 5 × 5 = 25 cm
^{2}
The area of the new square is 10 × 10 = 100 cm
^{2}
The area is 4 times bigger
Problem 12
On a field whose length is 25 meters and width is 12 meters a house was built the shape of a square whose side is 9 meters. What's the area of the garden?
Solution:
The field is a rectangle whose length is 25 meters and width is 12 meters. The area is L × W = 25 × 12 = 25 × 4 × 3 = 100 × 3 = 300 m
^{2}
The field covered by the house is a square with the side of 9 meters. The area is 9 × 9 = 81 m
^{2}
The garden's area will be 300 - 81 = 219 m
^{2}
Problem 13
What is the area of the blue zone?
Solution:
The area of the blue zone is half of the rectangle's area.
Area = (L × W) ÷ 2 = (12 × 9) ÷ 2 = 108 ÷ 2 = 54 m
^{2}
Problem 14
What is the area of the red zone?
Solution:
[AF] = 24 m
[DE] = 15 m
[BC] = [AF] - [DE] = 9 m
[FE] = 20 m
[AB] = 9 m
[CD] = [FE] - [AB] = 11 m
The area of the red zone is equal to the difference between the area of the rectangle with a length of 24 meters and a width of 20 meters and the area of the rectangle with a length of 11 meters and a width of 9 meters
Area = (24 × 20) - ( 11 × 9) = 480 - 99 = 381 m
^{2}
Problem 15
A park shaped like a square with a side of 30 meters has an alley with the width of 2 meters. What's the area of the green zone?
Solution:
The area of the park is 30 × 30 = 900 m
^{2}
The alley is shaped like a rectangle with a length of 30 m and a width of 2 m. Area is L × W = 30 × 2 = 60 m
^{2}
The green zone has an area of 900 - 60 = 840 m
^{2}
Problem 16
A TV has a length of 80 cm and a width of 50 cm. If the border is 5 cm thick, the area of the screen is
Solution:
The length of the screen is 80 - (5 + 5) = 80 - 10 = 70 cm, the width of the screen is 50 - (5 + 5) = 50 - 10 = 40 cm
The area of the screen is 70 × 40 = 2800 cm
^{2}
Problem 17
A rectangle with a length of 14 cm and a width of 10 cm is covered by black squares and blue squares with the same area. What is the total area of the blue squares?
Solution:
Because there are 5 squares on the width of the rectangle and 7 squares on its length, then the side of the square is 2 cm. The area of a square is 4 cm
^{2}
. There are 18 blue squares, so their area will be 4 × 18 = 72 cm
^{2}
Problem 18
Rectangle ABCD has a length of 8 cm and a width of 6 cm. What is the total area of the blue rectangles?
Solution:
The area of the rectangle ABCD is 48 cm
^{2}
. Rectangle ABCD is split into 4 equal rectangles. Thus, the area of rectangle AMOQ is 12 cm
^{2}
. Rectangle AMOQ is split into 4 equal rectangles. The area of a blue rectangle is 3 cm
^{2}
. The total area of the 2 blue rectangles is 6 cm
^{2}
.
Problem 19
The square has a side of 2 cm and the rectangle has a length of 9 cm and a width of 6 cm. What is the area of the red zone?
Solution:
The area of the square is 4 cm
^{2}
. It's split in 4 equal squares. The area of a small square is 1 cm
^{2}
, the area of the rectangle is 54 cm
^{2}
, so the area of the red zone is 54 - 1 = 53 cm
^{2}
.
Problem 20
A box whose every side is a rectangle has a length of 10 cm, a width of 6 cm and a height of 8 cm. What is the total area of the box?
Solution:
The sides of the box are equal in pairs. Two of the sides have edges of 10 cm and 6 cm.
Their area is (10 × 6) × 2 = 60 × 2 = 120 cm
^{2}
Two of the sides have edges of 10 cm and 8 cm.
Their area is (10 × 8) × 2 = 80 × 2 = 160 cm
^{2}
Two of the sides have edges of 8 cm and 6 cm.
Their area is (8 × 6) × 2 = 48 × 2 = 96 cm
^{2}
The total area is 120 + 160 + 96 = 376 cm
^{2}
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Copyright © 2005 - 2020.