Class 7 Maths Formulas

📘 Class 7 Maths

Algebra & Geometry — Formulas, Examples and Solutions

🟦 Part A: Algebra

1. Like Terms

Rule: Terms having the same variables with the same powers are called like terms.

3x + 5x = 8x

Example: 3x + 5x
Solution: 3x + 5x = 8x

Answer: 8x

2. Addition of Algebraic Expressions

Rule: Add the coefficients of like terms.

4x + 7 + 3x + 5

Solution:
4x + 3x + 7 + 5
= 7x + 12

Answer: 7x + 12

3. Subtraction of Algebraic Expressions

(8x + 7) - (3x + 2)

Solution:
= 8x + 7 - 3x - 2
= 5x + 5

Answer: 5x + 5

4. Multiplication of a Monomial

a(b + c) = ab + ac

Example: 3(x + 4)

Solution:
3(x + 4) = 3x + 12

Answer: 3x + 12

5. Multiplication of Two Monomials

ax × by = abxy

Example: 3x × 4y

Solution:
3x × 4y = 12xy

Answer: 12xy

6. Simple Linear Equation

Rule: Whatever operation is performed on one side must also be performed on the other side.

x + 7 = 15

Solution:
x = 15 − 7
x = 8

Answer: x = 8

7. Equation with Multiplication

3x = 21

Solution:
x = 21 ÷ 3
x = 7

Answer: x = 7

8. Equation with Division

x ÷ 5 = 6

Solution:
x = 6 × 5
x = 30

Answer: x = 30

🟩 Part B: Geometry

1. Complementary Angles

A + B = 90°

Example: One angle is 35°.

Solution:
90° − 35° = 55°

Answer: 55°

2. Supplementary Angles

A + B = 180°

Example: One angle is 120°.

Solution:
180° − 120° = 60°

Answer: 60°

3. Linear Pair

A + B = 180°

Example: One angle is 75°.

Solution:
180° − 75° = 105°

Answer: 105°

4. Vertically Opposite Angles

Vertically opposite angles are equal.

Example: If one angle is 65°, find its vertically opposite angle.

Solution: The vertically opposite angle is also 65°.

Answer: 65°

5. Sum of Angles of a Triangle

A + B + C = 180°

Example: Two angles are 50° and 60°.

Solution:
50° + 60° + C = 180°
C = 180° − 110°
C = 70°

Answer: C = 70°

6. Exterior Angle of a Triangle

Exterior angle = Sum of the two opposite interior angles

Example: Opposite interior angles are 50° and 70°.

Solution:
50° + 70° = 120°

Answer: 120°

7. Perimeter of a Rectangle

P = 2(l + b)

Example: Length = 8 cm, Breadth = 5 cm.

Solution:
P = 2(8 + 5)
= 2 × 13
= 26 cm

Answer: 26 cm

8. Area of a Rectangle

A = l × b

Example: Length = 10 cm, Breadth = 6 cm.

Solution:
A = 10 × 6
= 60 cm²

Answer: 60 cm²

9. Perimeter of a Square

P = 4 × side

Example: Side = 7 cm.

Solution:
P = 4 × 7
= 28 cm

Answer: 28 cm

10. Area of a Square

A = side²

Example: Side = 9 cm.

Solution:
A = 9²
= 81 cm²

Answer: 81 cm²

11. Area of a Triangle

A = ½ × base × height

Example: Base = 12 cm, Height = 5 cm.

Solution:
A = ½ × 12 × 5
= 6 × 5
= 30 cm²

Answer: 30 cm²

12. Area of a Parallelogram

A = base × height

Example: Base = 10 cm, Height = 6 cm.

Solution:
A = 10 × 6
= 60 cm²

Answer: 60 cm²

13. Circumference of a Circle

C = 2πr

Example: Radius = 7 cm. Take π = 22/7.

Solution:
C = 2 × 22/7 × 7
= 44 cm

Answer: 44 cm

14. Area of a Circle

A = πr²

Example: Radius = 7 cm. Take π = 22/7.

Solution:
A = 22/7 × 7 × 7
= 154 cm²

Answer: 154 cm²

⭐ Quick Revision Table

Topic	Formula / Rule
Complementary Angles	A + B = 90°
Supplementary Angles	A + B = 180°
Linear Pair	A + B = 180°
Vertically Opposite Angles	They are equal
Triangle Angles	A + B + C = 180°
Rectangle Perimeter	2(l + b)
Rectangle Area	l × b
Square Perimeter	4s
Square Area	s²
Triangle Area	½ × b × h
Parallelogram Area	b × h
Circle Circumference	2πr
Circle Area	πr²
Distributive Property	a(b + c) = ab + ac

📚 Class 7 Maths | Algebra & Geometry

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