Introduction to the Area of Triangles

Today, we are going to learn about the area of triangles. Understanding the area of a triangle is important in both maths and real-life situations, like when we want to find out how much paint we need for a triangular wall or how to cover a triangular garden.

What is the Area of a Triangle?

The area of a triangle is the amount of space inside it. We measure area in square units, like square centimetres (cm²) or square metres (m²).

How to Calculate the Area of a Triangle

The formula for finding the area of a triangle is:

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

  • Base: This is the bottom side of the triangle.
  • Height: This is a straight line from the top of the triangle to the base, making a right angle (90 degrees) with the base.

Step-by-Step Example

  1. Identify the Base and Height: Let’s say we have a triangle with a base of 6 cm and a height of 4 cm.
  2. Use the Formula: Plug the numbers into the formula. \text{Area} = \frac{1}{2} \times 6 , \text{cm} \times 4 , \text{cm}
  3. Calculate:
    • First, multiply the base and height: $6 \times 4 = 24$
    • Then, divide by 2: $24 \div 2 = 12$
  4. Conclusion: So, the area of this triangle is 12 cm².

Key Rules to Remember

  • Always use the base and the height that are perpendicular (90 degrees) to each other.
  • Make sure your measurements are in the same units before calculating.
  • The height can be outside of the triangle if it’s an obtuse triangle (one with an angle greater than 90 degrees).

Tips and Tricks

  • If you’re unsure which side is the base, remember that any side can be the base if you know the corresponding height.
  • Draw a right angle from the top of the triangle to the base to help visualize the height.

Practice Questions

Easy Level Questions

  1. Find the area of a triangle with a base of 5 cm and a height of 2 cm.
  2. What is the area of a triangle with a base of 10 cm and a height of 3 cm?
  3. Calculate the area of a triangle that has a base of 4 cm and a height of 4 cm.
  4. A triangle has a base of 8 cm and a height of 2 cm. What is its area?
  5. If a triangle has a base of 6 cm and a height of 6 cm, what is the area?
  6. Find the area of a triangle with a base of 7 cm and a height of 1 cm.
  7. What is the area of a triangle with a base of 12 cm and a height of 5 cm?
  8. Calculate the area of a triangle that has a base of 9 cm and a height of 3 cm.
  9. A triangle has a base of 3 cm and a height of 5 cm. What is its area?
  10. If a triangle has a base of 5 cm and a height of 10 cm, what is the area?

Medium Level Questions

  1. Find the area of a triangle with a base of 15 cm and a height of 8 cm.
  2. What is the area of a triangle with a base of 14 cm and a height of 6 cm?
  3. Calculate the area of a triangle that has a base of 20 cm and a height of 10 cm.
  4. A triangle has a base of 18 cm and a height of 4 cm. What is its area?
  5. If a triangle has a base of 16 cm and a height of 7 cm, what is the area?
  6. Find the area of a triangle with a base of 13 cm and a height of 9 cm.
  7. What is the area of a triangle with a base of 24 cm and a height of 5 cm?
  8. Calculate the area of a triangle that has a base of 22 cm and a height of 11 cm.
  9. A triangle has a base of 30 cm and a height of 6 cm. What is its area?
  10. If a triangle has a base of 25 cm and a height of 10 cm, what is the area?

Hard Level Questions

  1. Find the area of a triangle with a base of 35 cm and a height of 20 cm.
  2. What is the area of a triangle with a base of 40 cm and a height of 15 cm?
  3. Calculate the area of a triangle that has a base of 50 cm and a height of 25 cm.
  4. A triangle has a base of 45 cm and a height of 18 cm. What is its area?
  5. If a triangle has a base of 32 cm and a height of 14 cm, what is the area?
  6. Find the area of a triangle with a base of 60 cm and a height of 30 cm.
  7. What is the area of a triangle with a base of 55 cm and a height of 22 cm?
  8. Calculate the area of a triangle that has a base of 70 cm and a height of 28 cm.
  9. A triangle has a base of 80 cm and a height of 20 cm. What is its area?
  10. If a triangle has a base of 75 cm and a height of 15 cm, what is the area?

Answers

Easy Level Answers

  1. 5 cm x 2 cm = 5 cm²
  2. 10 cm x 3 cm = 15 cm²
  3. 4 cm x 4 cm = 8 cm²
  4. 8 cm x 2 cm = 8 cm²
  5. 6 cm x 6 cm = 18 cm²
  6. 7 cm x 1 cm = 3.5 cm²
  7. 12 cm x 5 cm = 30 cm²
  8. 9 cm x 3 cm = 13.5 cm²
  9. 3 cm x 5 cm = 7.5 cm²
  10. 5 cm x 10 cm = 25 cm²

Medium Level Answers

  1. 15 cm x 8 cm = 60 cm²
  2. 14 cm x 6 cm = 42 cm²
  3. 20 cm x 10 cm = 100 cm²
  4. 18 cm x 4 cm = 36 cm²
  5. 16 cm x 7 cm = 56 cm²
  6. 13 cm x 9 cm = 58.5 cm²
  7. 24 cm x 5 cm = 60 cm²
  8. 22 cm x 11 cm = 121 cm²
  9. 30 cm x 6 cm = 90 cm²
  10. 25 cm x 10 cm = 125 cm²

Hard Level Answers

  1. 35 cm x 20 cm = 350 cm²
  2. 40 cm x 15 cm = 300 cm²
  3. 50 cm x 25 cm = 625 cm²
  4. 45 cm x 18 cm = 405 cm²
  5. 32 cm x 14 cm = 224 cm²
  6. 60 cm x 30 cm = 900 cm²
  7. 55 cm x 22 cm = 605 cm²
  8. 70 cm x 28 cm = 980 cm²
  9. 80 cm x 20 cm = 800 cm²
  10. 75 cm x 15 cm = 562.5 cm²

I hope this helps you understand the area of triangles better! Remember to practice, and you’ll get the hang of it in no time!