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

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

Perimeter Of A Rectangle 

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

Area

The area is the space occupied by the figure. 

Area Of A Square

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

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.

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.

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?

Solution:

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?

Solution:

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? 

Solution: 

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

2. 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?

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. 

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.

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.

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:

$5 \text{ cm}$

3. 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.

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.

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. 

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. 

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. 

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. $81 \text{ m}^2$