chevron icon chevron icon chevron icon

Area And Perimeter 1

In this article, the learning objectives are:

  1. Finding the maximum number of squares that can be fitted/cut from a rectangle
  2. Finding unknown dimensions given area of a rectangle/square
  3. Finding unknown dimensions given perimeter of a rectangle/square

Let’s recap P3 Area and Perimeter first! 

 

Perimeter

The perimeter of a shape is the total distance around the shape.

Perimeter Of A Square

Perimeter Of A Square
 

\(\small \begin{aligned} \textsf{Perimeter Of A Square } &\mathsf{= \text{Length + Length + Length + Length}}\\[2ex] &\mathsf{= 4 \times \text{Length}} \end{aligned}\)

 

Perimeter Of A Rectangle 

Perimeter Of A Rectangle 
 

\(\small{ \textsf{Perimeter Of A Rectangle} = \textsf{Length + Breadth + Length + Breadth} }\)
 

Area

The area is the space occupied by the figure. 

Area Of A Square

Area Of A Square
 

\(\mathsf{\small{\text{Area Of A Square}= \text{Length} \times \text{Length}}}\)
 

Area Of A Rectangle

Area Of A Rectangle
 

\(\mathsf{\small{\text{Area Of A Rectangle}= \text{Length} \times \text{Breadth}}}\)

 

Question 1: 

Find the area and perimeter of the square below.

Find the area and perimeter of the square below.

Solution: 

Area of square
\(= 6 \text{ cm} \times 6 \text{ cm}\)
\(= 36 \text{ cm}^2 \)

Perimeter of square
\(= 4 \times 6 \text{ cm}\)
\(= 24 \text{ cm}\)

Answer: 

Area: \(36 \text{ cm}^2\)
Perimeter: \(24 \text{ cm}\)

 

Question 2: 

Find the area and perimeter of the rectangle below.

Find the area and perimeter of the rectangle below.

Solution: 

Area of rectangle
\(= 6 \text{ cm} \times 4 \text{ cm}\)
\(= 24 \text{ cm}^2\)

Perimeter of rectangle
\(= 6 \text{ cm} + 4 \text{ cm} + 6 \text{ cm} + 4 \text{ cm}\)
\(= 20 \text{ cm}\)

Answer: 

Area: \(24 \text{ cm}^2\)
Perimeter: \(20 \text{ cm}\)

 

  1. Finding the maximum number of squares that can be fitted / cut from a rectangle

To find the maximum number of squares that can be fitted/cut from an area, we will first find out the number of squares that are able to fit along the length and the breadth of that area.

 

Question 1: 

What is the maximum number of \(1 \text{ cm}\) squares that can be cut from the rectangle?

​ What is the maximum number of 1 cm squares that can be cut from the rectangle?  ​

Solution:

​ Number of 1 cm squares along the length of the rectangle  ​ 

Number of \(1 \text{ cm}\) squares along the length of the rectangle
\(= 5 \text{ cm} ÷ 1 \text{ cm}\)
\(= 5\)

Number of \(\small{1 \text{ cm}}\) squares along the breadth of the rectangle
\(= 3 \text{ cm} \div 1 \text{ cm}\)
\(= 3\)

Maximum number of squares that can be cut from the rectangle
\(= 5 \times 3\)
\(= 15\)

Answer:

\(15\) squares 

 

Question 2: 

What is the maximum number of \(2 \text{ cm}\) squares that can be cut from the rectangle?

​ What is the maximum number of 2 cm squares that can be cut from the rectangle?  ​

Solution:

​ Number of 2 cm squares along the length of the rectangle  ​

Number of \(2 \text{ cm}\) squares along the length of the rectangle
\(= 8 \text{ cm} \div 2 \text{ cm}\)
\(= 4\)

Number of \(\small{2 \text{ cm}}\) squares along the breadth of the rectangle
\(= 6 \text{ cm} \div 2 \text{ cm}\)
\(= 3\)

Maximum number of squares that can be cut from the rectangle
\(= 4 \times 3\)
\(= 12\)

Answer:

\(12\) squares 

 

Question 3:

What is the greatest number of \(4 \text{ cm}\) squares that can be cut from the rectangle? 

What is the greatest number of 4 cm squares that can be cut from the rectangle?                                

Solution: 

​ Number of 4 cm squares along the length of the rectangle  ​

Number of \(4 \text{ cm}\) squares along the length of the rectangle
\(= 16 \text{ cm} \div 4\text{ cm}\)
\(= 4\)

Number of \(4 \text{ cm}\) squares along the breadth of the rectangle
\(= 10 \text{ cm} \div 4 \text{ cm}\)
\(= 2 \text{ R } 2 \text{ cm}\)

We ignore the part which is represented by the remainder of \(2 \text{ cm}\) as no squares can be cut from it.

Greatest number of squares that can be cut from the rectangle
\(= 4 \times 2\)
\(= 8\)

Answer:

\(8\) squares

 

  1. Finding unknown dimensions given area of a rectangle / square

\(\mathsf{ \small{\text{Area Of A Rectangle} = \text{Length} \times \text{Breadth}} }\)

Therefore, 

\(\small \begin{align} \textsf{Length Of A Rectangle} &= \textsf{Area} \div \textsf{Breadth} \\[2ex] \textsf{Breadth Of A Rectangle} &= \textsf{Area} \div \textsf{Length} \end{align} ​\)

Question 1:

The area of a rectangle is \(126 \text{ cm}^2\). If its breadth is \(7 \text{ cm}\), what is the length of the rectangle?

​ The area of a rectangle is 126 cm2. If its breadth is 7 cm, what is the length of the rectangle?  ​

Solution: 

Length of the rectangle
\(= 126 \text{ cm}^2 ÷ 7 \text{ cm}\)
\(= 18 \text{ cm}\)

Answer:

\(18 \text{ cm}\)

 

Question 2: 

The area of a rectangle is \(72 \text{ cm}^2\). Given that the length of the rectangle is \(9 \text{ cm}\), find the breadth of the rectangle. 

The area of a rectangle is 72 cm2. Given that the length of the rectangle is 9 cm, find the breadth of the rectangle. 

Solution: 

Breadth of the rectangle
\(= 72 \text{ cm}^2 \div 9 \text{ cm}\)
\(= 8 \text{ cm}\)

Answer:

\(8 \text{ cm}\)

 

Question 3: 

The area of a square is \(64 \text{ cm}^2\). Find the length of one side of the square.

​ The area of a square is 64 cm2. Find the length of one side of the square.  ​

Solution: 

Since,

\(8 \text{ cm} \times 8 \text{ cm} = 64 \text{ cm}^2\),

Length of one side of each square \(= 8 \text{ cm}\)

Answer:

\(8 \text{ cm}\)

 

Question 4: 

The figure below is made up of \(3\) identical squares. Given that the total area of the figure is \(75 \text{ cm}^2\), find the length of one side of each square.

The figure below is made up of 3 identical squares. Given that the total area of the figure is 75 cm2, find the length of one side of each square.

Solution: 

Area of 1 square
\(= 75 \text{ cm}^2 \div 3\)
\(= 25 \text{ cm}^2\)

Since,

\(5 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2\),

Length of one side of each square \(= 5 \text{ cm}\)

Answer:

\(5 \text{ cm}\)

 

  1. Finding unknown dimensions given perimeter of a rectangle/square

\(\small\begin{align} \mathsf{\text{Perimeter Of Rectangle }} &\mathsf{= \text{Length + Length + Breadth + Breadth}}\\[2ex] \mathsf{\text{Length Of Rectangle }} &\mathsf{= \text{(Perimeter - Breadth - Breadth)} \div 2}\\[2ex] \mathsf{\text{Breadth Of Rectangle }} &\mathsf{= \text{(Perimeter - Length - Length)} \div 2} \end{align}\)

 

Question 1: 

The perimeter of a rectangle is \(36 \text{ cm}\). Given that its breadth is \(5 \text{ cm}\), find its length.

​ The perimeter of a rectangle is 36 cm. Given that its breadth is 5 cm, find its length.  ​

Solution:

Perimeter of a rectangle \(= \textsf{Length + Breadth + Length + Breadth}\)

Total length of 2 lengths
\(= 36 \text{ cm} - 5 \text{ cm} - 5 \text{ cm}\)
\(= 26 \text{ cm}\)

Length of rectangle
\(= 26 \text{ cm} \div 2\)
\(= 13 \text{ cm}\)

Answer:

\(13 \text{ cm}\)

 

Question 2: 

The perimeter of a rectangle is \(72 \text{ cm}\). Given that its length is \(24 \text{ cm}\), find its breadth.

​ The perimeter of a rectangle is 72 cm. Given that its length is 24 cm, find its breadth.  ​

Solution:

Perimeter of a rectangle \(= \textsf{Length + Breadth + Length + Breadth}\)

Total length of 2 lengths
\(= 72 \text{ cm} - 24 \text{ cm} - 24 \text{ cm}\)
\(= 24 \text{ cm}\)

Breadth of rectangle
\(= 24 \text{ cm} \div 2\)
\(= 12 \text{ cm}\)

Answer:

\(12 \text{ cm}\)

 

\(\small​\begin{align} \textsf{Perimeter of a square} &= \mathsf{4 \times Length} \\[2ex] \textsf{Length of one side of a square} &= \mathsf{Perimeter \div 4} \end{align}\)

 

Question 3: 

The perimeter of a square is \(60 \text{ cm}\). Find the length of one side of the square. 

​ The perimeter of a square is 60 cm. Find the length of one side of the square.   ​

Solution: 

Perimeter of a square \(= 4 \times \small{\textsf{ Length }}\)

Length of one side of the square
\(= 60 \text{ cm} \div 4\)
\(= 15 \text{ cm}\)

Answer:

\(15 \text{ cm}\)

 

Question 4: 

The area of a rectangular garden is \(168 \text{ m}^2\). Its breadth is 8 m. 

​ The area of a rectangular garden is 168 m2. Its breadth is 8 m.   ​

  1. Find the length of the garden. 
  2. Vincent jogged round the entire rectangular garden twice. Find the distance he jogged. 

Solution:

A. Length of the rectangle\(\begin{align} &= 168 \text{ m}^2 \div 8 \text{ m} \\[2ex] &= 21 \text{ m}  \end{align}\)

B. Perimeter of garden\(\begin{align}&= 21 \text{ m} + 8 \text{ m} + 21 \text{ m} + 8 \text{ m} \\[2ex] &= 58 \text{ m} \end{align}\)

Distance he jogged \(\begin{align}​​ &= 58 \text{ m} \times 2\\[2ex] &= 116 \text{ m}  \end{align}\)

Answer:

A. \(21 \text{ m}\)
B. \(116 \text{ m}\)

 

Question 5: 

Elaine jogged \(36 \text{ m}\) round a square sand pit. 

​ Elaine jogged 36m round a square sand pit.   ​

  1. Find the length of one side of the sand pit. 
  2. Find the area of the square sand pit. 

Solution: 

A. Length of one side of the sand pit\(\begin{align} &= 36 \text{ m} \div 4\\[2ex] &= 9 \text{ m} \end{align}\)

B. Area of the sand pit\(\begin{align} &= 9 \text{ m} \times 9 \text{ m}\\[2ex] &= 81 \text{ m}^2  \end{align}\)

Answer:

A. \(9 \text{ m}\)
B. \(81 \text{ m}^2\)

 


 

Continue Learning
Multiplication Whole Numbers
Multiplication And Division Decimals
Model Drawing Strategy Division
Fractions Factors And Multiples
Area And Perimeter 1 Line Graphs
Conversion Of Time  

 

Chương Trình
icon expand icon collapse Tiểu học
icon expand icon collapse
Đăng ký tư vấn ngay!
Đội ngũ Cố vấn giáo dục Geniebook sẽ liên hệ tư vấn đến ba mẹ ngay khi nhận được thông tin.
Đăng ký tư vấn ngay!
Geniebook CTA Illustration Geniebook CTA Illustration
Geniebook - Mở ra cơ hội học tập toàn cầu
Geniebook CTA Illustration Geniebook CTA Illustration
close icon
close icon
Geniebook - Mở ra cơ hội học tập toàn cầu
Đăng ký kiểm tra trình độ miễn phí ngay!
 
 
 
Xin lỗi
Oops! Có lỗi xảy ra rồi. Vui lòng tải lại trang!
Xin lỗi
Oops! Có lỗi xảy ra rồi. Vui lòng tải lại trang!
Chúng tôi đã nhận được yêu cầu của bạn!
Tư vấn viên sẽ liên hệ với bạn trong vài ngày tới để sắp xếp cho buổi demo!
Với việc cung cấp số điện thoại, bạn đã đồng ý cho Geniebook liên hệ tư vấn. Tham khảo thêm Chính sách bảo mật.
icon close
Default Wrong Input
Truy cập vào kho tài liệu của Geniebook
Bắt đầu hành trình học tập của bạn.
No Error
arrow down arrow down
No Error
Với việc cung cấp số điện thoại, bạn đã đồng ý cho Geniebook liên hệ tư vấn. Tham khảo thêm Chính sách bảo mật.
Success
Bắt đầu học thôi!
Tải tài liệu học tập ngay.
icon close
Error
Xin lỗi
Oops! Có lỗi xảy ra rồi. Vui lòng tải lại trang!