Heron's Formula: A = √(s(s-a)(s-b)(s-c)) where A is the area of the triangle and s is the semi-perimeter
Semi-perimeter: s = (a + b + c)/2
a, b, c are the sides of the triangle
Perimeter: P = 2s = a + b + c
Area of triangle: A = (base × height)/2, but Heron's formula is used when height is not known
Pythagoras theorem: a² + b² = c² for a right-angled triangle with sides a, b, c

🪤 The 5 Mistakes That Cost Marks

Not calculating the semi-perimeter correctly
Forgetting to take the square root ∈ Heron's formula
Using the wrong formula for the area of the triangle
Not checking if the given sides can form a triangle
Rounding off calculations too early, leading to incorrect answers

✏️ 3 Solved PYQs

Question 1: Find the area of a triangle with sides 5 cm, 12 cm, and 13 cm. Step 1: Calculate the semi-perimeter s = (5 + 12 + 13)/2 = 15 Step 2: Use Heron's formula A = √(15(15-5)(15-12)(15-13)) = √(15 × 10 × 3 × 2) = √900 = 30 Answer: 30 cm²
Question 2: Find the area of a triangle with base 10 cm and height 12 cm. Step 1: Use the formula A = (base × height)/2 = (10 × 12)/2 = 60 Answer: 60 cm²
Question 3: Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm. Step 1: Calculate the semi-perimeter s = (7 + 8 + 9)/2 = 12 Step 2: Use Heron's formula A = √(12(12-7)(12-8)(12-9)) = √(12 × 5 × 4 × 3) = √720 Answer: √720 or 12√5 cm²

🧠 The One Thing Most Students Get Wrong

Most students get the calculation of the semi-perimeter wrong, which leads to incorrect answers
Make sure to add all the sides of the triangle and divide by 2 to get the correct semi-perimeter
Use the correct formula for the area of the triangle, whether it's Heron's formula or the base-height formula

👁️ Ayush's Note

Always check if the given sides can form a triangle by using the triangle inequality theorem
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side
Use Heron's formula when the height of the triangle is not known, and use the base-height formula when the height is known

🔁 Last 5 Minutes Box

Last minute revision of Heron's formula and the semi-perimeter formula
Quick practice of calculating the area of a triangle using Heron's formula
Go through the common mistakes that can be made ∈ the calculation

📝 Practice MCQs

1. What is the semi-perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm?

A) 5 cm

B) 6 cm

C) 7 cm

D) 8 cm

Answer: B) 6 cm

2. What is the area of a triangle with base 8 cm and height 6 cm?

A) 20 cm²

B) 24 cm²

C) 30 cm²

D) 36 cm²

Answer: B) 24 cm²

3. What is the area of a triangle with sides 9 cm, 10 cm, and 11 cm?

A) 30 cm²

B) 35 cm²

C) 40 cm²

D) 45 cm²

Answer: C) 40 cm² (using Heron's formula)

4. Which of the following is a correct statement about the triangle inequality theorem?

A) The sum of the lengths of any two sides of a triangle must be less than the length of the third side

B) The sum of the lengths of any two sides of a triangle must be greater than the length of the third side

C) The sum of the lengths of any two sides of a triangle must be equal to the length of the third side

D) The sum of the lengths of any two sides of a triangle must be less than or equal to the length of the third side

Answer: B) The sum of the lengths of any two sides of a triangle must be greater than the length of the third side

5. What is the area of a triangle with sides 6 cm, 8 cm, and 10 cm?

A) 20 cm²

B) 24 cm²

C) 30 cm²

D) 40 cm²

Answer: B) 24 cm² (using Heron's formula)

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

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Continue your revision with these related guides:

Heron's Formula: A = √(s(s-a)(s-b)(s-c)) where A is the area of the triangle and s is the semi-perimeter
Semi-perimeter: s = (a + b + c)/2
a, b, c are the sides of the triangle
Perimeter: P = 2s = a + b + c
Area of triangle: A = (base × height)/2, but Heron's formula is used when height is not known
Pythagoras theorem: a² + b² = c² for a right-angled triangle with sides a, b, c

🪤 The 5 Mistakes That Cost Marks

Not calculating the semi-perimeter correctly
Forgetting to take the square root ∈ Heron's formula
Using the wrong formula for the area of the triangle
Not checking if the given sides can form a triangle
Rounding off calculations too early, leading to incorrect answers

✏️ 3 Solved PYQs

Question 1: Find the area of a triangle with sides 5 cm, 12 cm, and 13 cm. Step 1: Calculate the semi-perimeter s = (5 + 12 + 13)/2 = 15 Step 2: Use Heron's formula A = √(15(15-5)(15-12)(15-13)) = √(15 × 10 × 3 × 2) = √900 = 30 Answer: 30 cm²
Question 2: Find the area of a triangle with base 10 cm and height 12 cm. Step 1: Use the formula A = (base × height)/2 = (10 × 12)/2 = 60 Answer: 60 cm²
Question 3: Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm. Step 1: Calculate the semi-perimeter s = (7 + 8 + 9)/2 = 12 Step 2: Use Heron's formula A = √(12(12-7)(12-8)(12-9)) = √(12 × 5 × 4 × 3) = √720 Answer: √720 or 12√5 cm²

🧠 The One Thing Most Students Get Wrong

Most students get the calculation of the semi-perimeter wrong, which leads to incorrect answers
Make sure to add all the sides of the triangle and divide by 2 to get the correct semi-perimeter
Use the correct formula for the area of the triangle, whether it's Heron's formula or the base-height formula

👁️ Ayush's Note

Always check if the given sides can form a triangle by using the triangle inequality theorem
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side
Use Heron's formula when the height of the triangle is not known, and use the base-height formula when the height is known

🔁 Last 5 Minutes Box

Last minute revision of Heron's formula and the semi-perimeter formula
Quick practice of calculating the area of a triangle using Heron's formula
Go through the common mistakes that can be made ∈ the calculation

📝 Practice MCQs

1. What is the semi-perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm?

A) 5 cm

B) 6 cm

C) 7 cm

D) 8 cm

Answer: B) 6 cm

2. What is the area of a triangle with base 8 cm and height 6 cm?

A) 20 cm²

B) 24 cm²

C) 30 cm²

D) 36 cm²

Answer: B) 24 cm²

3. What is the area of a triangle with sides 9 cm, 10 cm, and 11 cm?

A) 30 cm²

B) 35 cm²

C) 40 cm²

D) 45 cm²

Answer: C) 40 cm² (using Heron's formula)

4. Which of the following is a correct statement about the triangle inequality theorem?

A) The sum of the lengths of any two sides of a triangle must be less than the length of the third side

B) The sum of the lengths of any two sides of a triangle must be greater than the length of the third side

C) The sum of the lengths of any two sides of a triangle must be equal to the length of the third side

D) The sum of the lengths of any two sides of a triangle must be less than or equal to the length of the third side

Answer: B) The sum of the lengths of any two sides of a triangle must be greater than the length of the third side

5. What is the area of a triangle with sides 6 cm, 8 cm, and 10 cm?

A) 20 cm²

B) 24 cm²

C) 30 cm²

D) 40 cm²

Answer: B) 24 cm² (using Heron's formula)

🚀 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: