A quadrilateral is a 4-sided polygon with 4 vertices and 4 angles.
Sum of interior angles of a quadrilateral = (n-2) × 180°, where n = 4
Sum of interior angles of a quadrilateral = (4-2) × 180° = 2 × 180° = 360°
Sum of exterior angles of a quadrilateral = 360°
A quadrilateral with all sides equal is called a rhombus.
A quadrilateral with all sides equal and all angles equal is called a square.
Diagonals of a rectangle bisect each other and are equal ∈ length.
Diagonals of a rhombus bisect each other at right angles.
Diagonals of a square bisect each other at right angles and are equal ∈ length.
Area of a quadrilateral = (1/2) × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals
Area of a quadrilateral = (1/2) × (sum of the products of the adjacent sides and the sines of the included angles)

🪤 The 5 Mistakes That Cost Marks

Not checking if the given quadrilateral is a special type, such as a rectangle or a rhombus.
Not using the properties of diagonals, such as the fact that they bisect each other ∈ a rectangle or a rhombus.
Not using the formula for the area of a quadrilateral ∈ terms of its diagonals.
Not using the properties of angles, such as the fact that the sum of the interior angles is 360°.
Not checking if the given quadrilateral is cyclic, and if so, using the properties of cyclic quadrilaterals.

✏️ 3 Solved PYQs

In a quadrilateral ABCD, the sum of the interior angles is 360°. If ∠A = 80°, ∠B = 110°, and ∠C = 90°, find ∠D. ∠D = 360° - (∠A + ∠B + ∠C) = 360° - (80° + 110° + 90°) = 360° - 280° = 80°
In a rhombus ABCD, the lengths of the diagonals are 6 cm and 8 cm. Find the area of the rhombus. Area = (1/2) × d₁ × d₂ = (1/2) × 6 × 8 = 24 cm²
In a rectangle ABCD, the length of one side is 5 cm and the length of the other side is 3 cm. Find the area of the rectangle. Area = length × breadth = 5 × 3 = 15 cm²

🧠 The One Thing Most Students Get Wrong

The difference between a rectangle and a rhombus. A rectangle has all angles equal to 90°, while a rhombus has all sides equal.

👁️ Ayush's Note

To solve problems on quadrilaterals, first check if the given quadrilateral is a special type, such as a rectangle or a rhombus.
Use the properties of diagonals, such as the fact that they bisect each other ∈ a rectangle or a rhombus.
Use the formula for the area of a quadrilateral ∈ terms of its diagonals.
Check if the given quadrilateral is cyclic, and if so, use the properties of cyclic quadrilaterals.

🔁 Last 5 Minutes Box

Sum of interior angles of a quadrilateral = 360°
Sum of exterior angles of a quadrilateral = 360°
Diagonals of a rectangle bisect each other and are equal ∈ length.
Diagonals of a rhombus bisect each other at right angles.
Area of a quadrilateral = (1/2) × d₁ × d₂

📝 Practice MCQs

1. What is the sum of the interior angles of a quadrilateral?

A) 180°

B) 270°

C) 360°

D) 450°

Answer: C) 360°.

2. What is the area of a rhombus with diagonals of length 6 cm and 8 cm?

A) 12 cm²

B) 20 cm²

C) 24 cm²

D) 30 cm²

Answer: C) 24 cm².

3. What is the length of the diagonal of a rectangle with sides of length 5 cm and 3 cm?

A) 5 cm

B) 3 cm

C) √(5² + 3²) = √(25 + 9) = √34

D) 8 cm

Answer: C) √34.

4. What is the sum of the exterior angles of a quadrilateral?

A) 180°

B) 270°

C) 360°

D) 450°

Answer: C) 360°.

5. What is the area of a rectangle with sides of length 5 cm and 3 cm?

A) 10 cm²

B) 12 cm²

C) 15 cm²

D) 20 cm²

Answer: C) 15 cm².

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

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A quadrilateral is a 4-sided polygon with 4 vertices and 4 angles.
Sum of interior angles of a quadrilateral = (n-2) × 180°, where n = 4
Sum of interior angles of a quadrilateral = (4-2) × 180° = 2 × 180° = 360°
Sum of exterior angles of a quadrilateral = 360°
A quadrilateral with all sides equal is called a rhombus.
A quadrilateral with all sides equal and all angles equal is called a square.
Diagonals of a rectangle bisect each other and are equal ∈ length.
Diagonals of a rhombus bisect each other at right angles.
Diagonals of a square bisect each other at right angles and are equal ∈ length.
Area of a quadrilateral = (1/2) × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals
Area of a quadrilateral = (1/2) × (sum of the products of the adjacent sides and the sines of the included angles)

🪤 The 5 Mistakes That Cost Marks

Not checking if the given quadrilateral is a special type, such as a rectangle or a rhombus.
Not using the properties of diagonals, such as the fact that they bisect each other ∈ a rectangle or a rhombus.
Not using the formula for the area of a quadrilateral ∈ terms of its diagonals.
Not using the properties of angles, such as the fact that the sum of the interior angles is 360°.
Not checking if the given quadrilateral is cyclic, and if so, using the properties of cyclic quadrilaterals.

✏️ 3 Solved PYQs

In a quadrilateral ABCD, the sum of the interior angles is 360°. If ∠A = 80°, ∠B = 110°, and ∠C = 90°, find ∠D. ∠D = 360° - (∠A + ∠B + ∠C) = 360° - (80° + 110° + 90°) = 360° - 280° = 80°
In a rhombus ABCD, the lengths of the diagonals are 6 cm and 8 cm. Find the area of the rhombus. Area = (1/2) × d₁ × d₂ = (1/2) × 6 × 8 = 24 cm²
In a rectangle ABCD, the length of one side is 5 cm and the length of the other side is 3 cm. Find the area of the rectangle. Area = length × breadth = 5 × 3 = 15 cm²

🧠 The One Thing Most Students Get Wrong

The difference between a rectangle and a rhombus. A rectangle has all angles equal to 90°, while a rhombus has all sides equal.

👁️ Ayush's Note

To solve problems on quadrilaterals, first check if the given quadrilateral is a special type, such as a rectangle or a rhombus.
Use the properties of diagonals, such as the fact that they bisect each other ∈ a rectangle or a rhombus.
Use the formula for the area of a quadrilateral ∈ terms of its diagonals.
Check if the given quadrilateral is cyclic, and if so, use the properties of cyclic quadrilaterals.

🔁 Last 5 Minutes Box

Sum of interior angles of a quadrilateral = 360°
Sum of exterior angles of a quadrilateral = 360°
Diagonals of a rectangle bisect each other and are equal ∈ length.
Diagonals of a rhombus bisect each other at right angles.
Area of a quadrilateral = (1/2) × d₁ × d₂

📝 Practice MCQs

1. What is the sum of the interior angles of a quadrilateral?

A) 180°

B) 270°

C) 360°

D) 450°

Answer: C) 360°.

2. What is the area of a rhombus with diagonals of length 6 cm and 8 cm?

A) 12 cm²

B) 20 cm²

C) 24 cm²

D) 30 cm²

Answer: C) 24 cm².

3. What is the length of the diagonal of a rectangle with sides of length 5 cm and 3 cm?

A) 5 cm

B) 3 cm

C) √(5² + 3²) = √(25 + 9) = √34

D) 8 cm

Answer: C) √34.

4. What is the sum of the exterior angles of a quadrilateral?

A) 180°

B) 270°

C) 360°

D) 450°

Answer: C) 360°.

5. What is the area of a rectangle with sides of length 5 cm and 3 cm?

A) 10 cm²

B) 12 cm²

C) 15 cm²

D) 20 cm²

Answer: C) 15 cm².

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides: