Study P4 Mathematics Maths - Area and Perimeter - Geniebook

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

\(\begin{align} &= \text{Length + Length + Length + Length} \\[2ex] &= 4 \times \text{Length} \end{align}\)

 

Perimeter Of A Rectangle 

\(= \text{Length + Breadth + Length + Breadth}\)

 

Area

The area is the space occupied by the figure. 

Area Of A Square

\(\begin{align} = \text{Length} \times \text{Length}  \end{align}\)

 

Area Of A Rectangle

\(\begin{align} = \text{Length} \times \text{Breadth}  \end{align}\)

 

Question 1: 

Find the area and perimeter of the square below.

Solution: 

Area of square 

\(\begin{align} &= 6 \;cm \times 6 \;cm \\[2ex] &= 36 \;cm^2 \end{align}\)

Perimeter of square

\(\begin{align} &= 4 \times 6 \;cm \\[2ex] &= 24 \;cm  \end{align}\)

Answer: 

Area: \(36 \;cm^2\)

Perimeter: \(24 \;cm\)

 

 

Question 2: 

Find the area and perimeter of the rectangle below.

Solution: 

Area of rectangle

\(\begin{align} &= 6 \;cm \times 4 \;cm \\[2ex] &= 24 \;cm^2 \end{align}\)

Perimeter of rectangle

\(\begin{align} &= 6 \;cm + 4 \;cm + 6 \;cm + 4 \;cm \\[2ex] &= 20 \;cm \end{align}\)

Answer: 

Area: \(24 \;cm^2\)

Perimeter: \(20 \;cm\)

 

 

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 \(1 \;cm\) squares that can be cut from the rectangle?

 

Solution:

 

Number of \(1 \;cm\) squares along the length of the rectangle

\(\begin{align} &= 5 \;cm ÷ 1 \;cm \\[2ex] &= 5 \end{align} ​\)

Number of \(1 \;cm\) squares along the breadth of the rectangle

\(\begin{align} &= 3 \;cm ÷ 1 \;cm \\[2ex] &= 3 \end{align} ​\)

Maximum number of squares that can be cut from the rectangle

\(\begin{align} &= 5 \times 3 \\[2ex] &= 15 \end{align}\)

Answer:

\(15\) squares 

 

 

Question 2: 

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

\(\begin{align} &= 8 \;cm \div 2 \;cm \\[2ex] &= 4 \end{align}\)

Number of \(2 \;cm\) squares along the breadth of the rectangle

\(\begin{align} &= 6 \;cm \div 2 \;cm \\[2ex] &= 3 \end{align}\)

Maximum number of squares that can be cut from the rectangle

\(\begin{align} &= 4 \times 3 \\[2ex] &= 12 \end{align}\)

Answer:

\(12\) squares 

 

 

Question 3:

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

\(\begin{align} &= 16 \;cm \div 4\;cm \\[2ex] &= 4 \end{align}\)

Number of \(4 \;cm\) squares along the breadth of the rectangle

\(\begin{align} &= 10 \;cm \div 4\;cm \\[2ex] &= 2\;R \;2\;cm \end{align}\)

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

Greatest number of squares that can be cut from the rectangle

\(\begin{align} &= 4 \times 2 \\[2ex] &= 8 \end{align}\)

Answer:

\(8\) squares 

 

 

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

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

Therefore, 

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

 

Question 1:

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

                             

 

Solution: 

Length of the rectangle

\(\begin{align} &= 126 \;cm^2 ÷ 7 \;cm \\[2ex] &= 18 \;cm \end{align}\)

Answer:

\(18 \;cm\)

 

 

Question 2: 

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

\(\begin{align}​​ &= 72 \;cm^2 \div 9 \;cm\\[2ex] &= 8 \;cm  \end{align}\)

Answer:

\(8 \;cm\)

 

 

Question 3: 

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

Solution: 

Since \(8 \;cm \times 8 \;cm = 64 \;cm^2\),

Length of one side of each square \(= 8 \;cm\)

Answer:

\(8 \;cm \)

 

 

Question 4: 

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

Solution: 

Area of 1 square

\(\begin{align}​​ &= 75 \;cm^2 \div 3\\[2ex] &= 25 \;cm^2  \end{align}\)

Since \(5 \;cm \times 5 \;cm = 25 \;cm^2\),

Length of one side of each square \(= 5 \;cm\)

Answer:

\(5 \;cm\)


 

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

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

 

Question 1: 

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

Solution: 

\(\begin{align}​​ \text{Perimeter of a rectangle} &= \text{Length + Breadth + Length + Breadth} \\[3ex] \text{Total length of 2 lengths} &= 36 \;cm - 5 \;cm - 5 \;cm \\[2ex] &= 26 \;cm\\[3ex] \text{Length of rectangle} &= 26 \;cm ÷ 2 \\[2ex] &= 13 \;cm \end{align}\)

Answer:

\(13 \;cm\)

 

 

Question 2: 

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

Solution:

\(\begin{align}​​ \text{Perimeter of a rectangle} &= \text{Length + Breadth + Length + Breadth} \\[3ex] \text{Total length of 2 breadths} &= 72 \;cm - 24 \;cm - 24 \;cm \\[2ex] &= 24 \;cm\\[3ex] \text{ Breadth of rectangle} &= 24 \;cm ÷ 2 \\[2ex] &= 12 \;cm \end{align}\)

Answer:

\(12 \;cm\)

 

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

 

Question 3: 

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


 

Solution: 

Perimeter of a square \(= 4 \;×\) Length 
Length of one side of the square\(\begin{align}​​\\[2ex] &= 60 \;cm \div 4\\[2ex] &= 15 \;cm \end{align}\)

Answer:

\(15 \;cm\)


 

Question 4: 

The area of a rectangular garden is \(168 \;m^2\). 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:

  1. Length of the rectangle\(\begin{align}​​\\[2ex] &= 168 \;m^2 \div 8 \;m \\[2ex] &= 21 \;m  \end{align}\)
  2. Perimeter of garden\(\begin{align}​​\\[2ex] &= 21 \;m + 8 \;m + 21 \;m + 8 \;m \\[2ex] &= 58 \;m \end{align}\)
    Distance he jogged \(\begin{align}​​\\[2ex] &= 58 \;m \times 2\\[2ex] &= 116 \;m  \end{align}\)

Answer:

  1. \(21 \;m\)

Answer:

  1. \(116 \;m\)



 

Question 5: 

Elaine jogged \(36 \;m\) 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: 

  1. Length of one side of the sand pit\(\begin{align}​​\\[2ex] &= 36 \;m \div 4\\[2ex] &= 9 \;m  \end{align}\)
  2. Area of the sand pit\(\begin{align}​​\\[2ex] &= 9 \;m \times 9 \;m\\[2ex] &= 81 \;m^2  \end{align}\)

Answer:

  1. \(9 \;m\)

Answer:

  1. \(81 \;m^2\)


 

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