Grade Six Mathematics
Answers to last week’s exercise
Exercise 1 7. 1. 2 half litres 8. 2. 6 half litres 3. 15 half litres 4. 19 half litres 5. 1L = ¼ L + ¼ L + ¼ L + ¼
L
Exercise 2 1. 12,000 mL 2. 8,000 mL 3. 8,700 mL 4. 5,500 mL 5. 2,370 mL 6. 3,450 mL 8,889 mL 4,754 mL
Exercise 3 1) 9L 12.35 L 4.376 L 0.03 L 4.226 L 0.95 L 6.547 L 4L
2.31 L 7.79 L
Greetings, boys and girls. I hope your week at school was fruitful. In our previous session, we explored the concept of measurement, specifically converting capacity units. This week, we will be examining the concept of the perimeter of plane shapes. Let’s begin.
Perimeter
The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
What are plane shapes?
Plane shapes are two-dimensional shapes. They have a breadth and a width but do not have a thickness. The basic plane shapes are square, rectangle, triangle, circle, and polygons.
Let us now examine how we can calculate the perimeter of a square.
Calculating the perimeter of a square
Ok boys and girls, let’s engage in some critical thinking! Test your knowledge by answering the following questions:
What do you know about a square? How many sides does a square have? Are all the sides equal? Considering that we understand the perimeter is the total distance around the shape, can you brainstorm a way to calculate the perimeter of a square?
Let’s check if your responses to those questions are accurate.
What is the perimeter of a square?
The perimeter of a square is the total length of all the sides of the square. Hence, we can find the perimeter of a square by adding all its four sides. All the sides of a square are equal.
Formula:
Perimeter of a square= Length + Length + Length + Length
OR
Perimeter of square= 4 x L (4 multiplied by one side)
Let us apply the formula to an example:
Example 1
Calculate the perimeter of a square with each side measuring 2cm.
Solution: Given: Side length of square = 2cm.
We know, using the perimeter of a square formula,
Perimeter of square = 4 × Side
⇒ 4 × 2 = 8cm
Boys and girls, do you understand? For further clarity, review the example above.
Let us work a few.
Exercise 1
1. Calculate the distance around a square of side 8cm. 2. Tom walked around a square field of side 20cm. what distance did he cover?
3. How much wire is needed to fence a square field of side 14m?
4. Calculate the perimeter of a square tile of side 60cm.
5. Sarah walked 15m. Calculate the
Exercise 2
5 times around a square field of side total distance she walked.
I’m confident that you performed excellently in that task. Well done! Now, let’s proceed.
In certain cases, we are provided with the perimeter and tasked with determining the length of a single side of the square. Do you know how we can attempt to do so? Let’s find out!
Given the perimeter of a square to find one side
To calculate the length of one side of the square when given the perimeter, we use the following formula:
Formula: Perimeter ÷ 4 or
Let us apply this in an example:
Example 1
Given that the perimeter of a square is 20cm, calculate the length of one side. Formula: Perimeter ÷ 4 = 20/4 = 5cm
Hence, the length of one side of the square is 5cm.
Let’s practice working a few.
Great job, boys and girls! Let us examine another plane shape.
Let me arouse your reasoning ability once more! What do you know about a rectangle? How many sides does a rectangle have? Are all the sides equal? Since we are now aware that the perimeter is the distance around the shape, can you think of a way we can derive the perimeter of a rectangle?
Let’s see if your responses to those questions are correct.
The perimeter of a rectangle
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. The opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.
Formula:
Perimeter of rectangle= L+B+L+B
OR
Perimeter of rectangle= (L+B) × 2
Let us examine an example:
Calculate the perimeter of a rectangle of length 12cm and breadth 7cm.
P= L+B+L+B
P= 12cm + 7cm+ 12cm + 7cm = 38 cm
Let us now apply the knowledge we have gained, by completing the following activity: