Important Formulas: Grandmother’s Quilt | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Perimeter

• Derived from Greek words: peri (around) + metron (measure).

• Definition: Distance around a plane figure (sum of all sides).

• Units: cm, m, km, etc.

• Key Note: Perimeter tells about the boundary, not the inside.

Formulas for Perimeter

1. Rectangle:

• Perimeter = 2 × (length + width)

• P = 2(l + w)

Example 1: The length of the sides AB and CD of the rectangle ABCD are 3 cm each and the length of the sides BC and DA are 6 cm each. Find its perimeter.

Perimeter of rectangle ABCD,
= 3 cm + 6 cm + 3 cm + 6 cm = 18 cmUsing the formula,
Perimeter of the rectangle ABCD = 2(l + b)
= 2 × (6 + 3) cm
= 2 × 9 cm = 18 cm
Thus, the perimeter of the rectangle ABCD is 18 cm.

2. Square

• Perimeter = 4 × side

• P = 4 × a

Example 2: The measure of a side of a square is 7 cm. Find the perimeter of the square.

The perimeter of the square = 4 × length of one side
= 4 × 7 cm = 28 cmThus, the perimeter of the square is 28 cm.

3. Triangle

• Perimeter = sum of all sides

• P = a + b + c

Example 3: Triangle ABC is an equilateral triangle with all the sides measuring 6 cm each. Find its perimeter.

Perimeter of an equilateral triangle
= 3 × length of one side= 3 × 6 cm = 18 cm
Thus, the perimeter of the triangle ABC is 18 cm.

4. Regular Polygon (all sides equal)

• Perimeter = Number of sides × Length of one side

Area

• Definition: Amount of space covered by a plane figure.

• Units: mm², cm², m², km², etc.

• Key Note: Area tells about the inside of a shape, not the boundary.

Finding Area Using Grids

Step 1: Place shape on a square grid.

Step 2: Count all full squares inside.

Step 3: Combine half squares to make full squares.

Count the total number of fully shaded squares and combine the half shaded squares to make 1 square unit.

Step 4: Total unit squares = Area.

There are 2 shaded squares and 4 halves. The 4 halves can be combined to make 2 more shaded squares:

Example 4: Find the area of each of the following regions by counting squares.

Mark the squares in the figures:
(a) Since there are 7 squares in the figure,
∴ Area of the given figure = 7 square units.
(b) Since there are 8 squares in the figure,
∴ Area of the given figure = 8 square units.

Area Formulas

1. Rectangle

• Area = Length × Width

• A = l × w

Example 7: Find the area of a rectangle with length 12 cm and breadth 4 cm.

Area of rectangle = l × w
= 12 cm × 4 cm = 48 sq cm.

2. Square

• Area = Side × Side

• A = a²

Example 9: Find the area of a square field of side length 70 m?

Area of square = Side × Side  
= 70 m × 70 m = 4900 sq m.

Connection Between Perimeter and Area

• Perimeter = boundary length

• Area = space inside

• Both can be found using length and breadth for rectangles and side for squares.