Maths Perimeter and Area part 12 (Area of Circle) CBSE Class 7 Mathematics VII

TL;DR

Learn how to calculate the area of a circle by dividing it into sectors and forming a parallelogram, with the formula A = πr^2.

Transcript

hello friends this video on perimeter and area part 12 is brought to you by exam fire comm normal for your prom exams sir that was all about self confidence now let us focus on area of a circle how do we calculate the area of a circle so let's say you have the circle and you have to find out the total region that is enclosed within the circle so ba... Read More

Key Insights

• 💁 The area of a circle can be found by dividing it into equal sectors and forming a parallelogram.
• ⚾ The base of the parallelogram is equal to half the circumference of the circle.
• 🟰 The height of the parallelogram is equal to the radius of the circle.
• ⭕ The formula for the area of a circle is derived as A = πr^2.
• 🆘 Understanding the derivation of the formula helps in deeper comprehension and application of the concept.
• 🥶 Exam Fire offers free quality education with a four-step learning process.
• 😷 Their content includes video lessons, the ability to ask questions, reference notes, and free online tests.

Questions & Answers

Q: How is the area of a circle calculated?

The area of a circle is calculated by using the formula A = πr^2, where r represents the radius of the circle. This formula is derived by dividing the circle into sectors and forming a parallelogram.

Q: Why is the base of the parallelogram equal to half the circumference of the circle?

The base of the parallelogram is equal to half the circumference of the circle because the eight sectors that form the parallelogram contribute to the full boundary of the circle. Therefore, to consider only four sectors, the base is halved.

Q: What is the height of the parallelogram in this case?

The height of the parallelogram is equal to the radius of the circle. It is represented by a line drawn perpendicular to the base from the opposite vertex, which is essentially the radius of the circle.

Q: Why is it important to understand the derivation of the area of a circle formula?

It is important to understand the derivation of the formula to have a clear concept of how the formula is derived and why it works. This understanding can help in solving various real-life problems and ensures a deeper grasp of the mathematical concept.

Summary & Key Takeaways

• The video explains how to calculate the area of a circle by dividing it into eight equal sectors and arranging them to form a parallelogram.

• The base of the parallelogram is equal to half the circumference of the circle, and the height is the radius.

• By applying the formula for the area of a parallelogram, A = base x height, the formula for the area of a circle is derived as A = πr^2.