Grandmother's Quilt Chapter Notes | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Preetha and Adrit’s grandmother made a quilt cover using old clothes. Now she wants to decorate it with lace, using two different colours. She decides to use two different coloured laces. How much lace of each kind will be needed to cover the entire border? 

All these types of questions referring to the length around a plane figure are answered by ‘‘Perimeter’’.

What is Perimeter?

The word perimeter is derived from two Greek words: peri, meaning around, and metron, meaning measure.

Thus, we measure the perimeter of a plane figure by adding the lengths of its sides.
Perimeter is the distance around a plane figure or the length of the boundary of a plane figure.

Observe the following example:

• If the perimeter of the quilt is 90 units, and the grandmother wants to use two different coloured laces, and we have the following options- red colour 40 units, green colour 50 units and blue colour 25 units, then
• Lace required in red colour = 40 units
• Lace required in green colour = 50 units
• Total lace used = 40 + 50 = 90 units

Remember:

• Write units for perimeter (cm, m, km).
• The perimeter tells us the length around and not about the inside.

Perimeter of a Rectangle

A rectangle is a plane figure whose opposite sides (facing each other) are of equal lengths.
So, we have two equal lengths and two equal breadths.
Perimeter of a rectangle = length + breadth + length + breadth
= length + length + breadth + breadth
= 2 × length + 2 × breadth
= 2 × (length + breadth) = 2 × (l + b)

Perimeter of rectangle = 2 × (length + breadth)

Perimeter of a Square

A square is a plane figure whose all four sides are of equal lengths.
Perimeter of a square = side + side + side + side
= 4 × side

Perimeter of a square = 4 × length of one side

Perimeter of a Triangle

A triangle is a plane figure with three sides.
So, the perimeter of a triangle is the sum of the lengths of its three sides.

Perimeter of a triangle = A+ B+ C

Perimeter of a triangle = side₁ + side₂ + side₃

Perimeter of a Shape with Equal Sides

Such a shape is where all sides are equal (like a regular polygon or regular hexagon).

To find its perimeter, we add the lengths of all the equal sides.

Perimeter = A + A + A + A + A

Perimeter = Number of sides × Length of one side

Now that we know how to measure the length around a shape, let’s think about how much space a shape covers inside.

Preetha and Adrit’s grandmother is making a rug with square patches. Look at the picture of the rug - can you count how many patches she has used? Each patch takes up some space, and all the patches together cover the whole rug.

Preetha and Adrit also tried covering their table using different shapes:

• Preetha used triangles and circles.
• Adrit used squares and rectangles.

They found that triangle, square and rectangle shapes cover the top of the table without gaps and overlaps. Circle shape leaves gaps.

TWENTY triangles cover Table 1.

EIGHT squares cover Table 3.

SIX rectangles cover Table 4

You have been introduced to the concept of area in Class IV. Let us revise. How many marble tiles can fit on the floor or wall? How much paint is needed for the wall? All these questions refer to the surface within the boundary and are answered by Area.

What is Area?

The area of a shape is the amount of space it covers.

It refers to the flat surface taken by a plane figure. The region covered by the triangles, squares or rectangles is called the "area" of the table. To find the area of a region, we usually fill it with shapes that tile well — like squares, rectangles, and triangles. Circles do not tile perfectly because they leave spaces in between.

Units of Measurement of Area

The units used to measure area are based on the units of length, i.e., mm, cm, m and km.

This is an area equal to 1 square millimetre (mm²).

This is an area equal to 1 square centimetre (cm²).

represent other units of measuring area ,such as 1 square metre (m2) and 1 square kilometre (km2).
The unit used for measuring the area depends on the size of the area being measured.
For example, the areas of the following shapes are usually measured as under:

Remember:

• Write units for area (cm², m², km²).
• The area tells us the space inside a shape, not the length around it.

Finding Area using Grids

• A grid is made of small squares of equal size.
• Each small square is called 1 unit square.
• To find the area of a shape, we count how many unit squares it covers.

Steps to find the area using grids:

1. Place the shape on the square grid.
2. Count all the full squares inside the shape.
3. If there are half squares, put two halves together to make one full square.
4. The total number of unit squares = Area of the shape.

Let us do

Area of Garden A = _____ cm square
Area of Garden B = _____ cm square

Sol: Area of Garden A = 10 cm²
           Area of Garden B = 12 cm²

Explanation:
Each small square in the grid is 1 cm².
When we count all the shaded squares in Garden A, we get 10.
When we count all the shaded squares in Garden B, we  get 12.

2. Is the area of shape (a) less than the area of shape (b) given below? Discuss.

Preetha and Adrit’s grandmother is making another square patchwork. She arranges the patches as shown below. Can you guess how many patches she will need? How did you find it?

Did you notice that 6 is the length of one side and 4 is the length of the non-equal side of the rectangle?

Sol:  Yes, the area of shape (a) is less than the area of shape (b) because shape (b) covers more square units on the grid.

For the square patchwork, there are 6 rows with 4 patches in each row.
Total patches = $\mathrm{(6}\times \mathrm{4)\; square\; cm}=246\; \backslash times\; 4\; =\; 24$ $\mathrm{square\; cm}$
Here, 6 is the length and 4 is the breadth of the rectangle, showing that:

$Area\; of\; a\; RectangleBreadth\backslash text\{Area\; of\; a\; Rectangle\}\; =\; \backslash text\{Length\}\; \backslash times\; \backslash text\{Breadth\}$Area of a Rectangle = Length × Breadth

Similarly, we can also find the perimeter of the rectangular shape.

Perimeter = Length + Length +Breadth + Breadth 
= 2 × Length + 2 × Breadth

Area of a Rectangle

A rectangle is a plane figure whose opposite sides are equal.
So, it has two equal lengths and two equal breadths.
The area is the space covered inside the rectangle.

$Area\; of\; a\; rectanglebreadth\backslash text\{Area\; of\; a\; rectangle\}\; =\; \backslash text\{length\}\; \backslash times\; \backslash text\{breadth\}$Area of a rectangle = length × breadth

Area of a Square

A square is a plane figure whose all four sides are equal.
The area is the space covered inside the square.

$Area\; of\; a\; squareside\backslash text\{Area\; of\; a\; square\}\; =\; \backslash text\{side\}\; \backslash times\; \backslash text\{side\}$Area of a square = side × side = side²

Example:

1. Find the length of a rectangle if its area = 120 cm² and its breadth = 10 cm 
Sol: Area = 120 cm2, Breadth = 10 cm ∴ Length = Area ÷ Breadth = 120 cm2 ÷ 10 cm = 12 cm. 

2. The perimeter of a square is 24 cm. Find its area. 
Sol: To find the area, we need the side of the square. 
          Side of the square = Perimeter ÷ 4 = 24 cm ÷ 4 = 6 cm 
          ∴ Area = side × side = 6 cm × 6 cm = 36 cm2.