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Find the best tutors and institutes for Class 10 Tuition
Find Best Class 10 Tuition
Find the best tutors and institutes for Class 10 Tuition
In CBSE Class 10 Mathematics, the chapter "Areas Related to Circles" takes a step further from basic formulas by introducing "Problems based on combinations of plane figures." This concept bridges the gap between simple 2D geometry and real-world spatial reasoning. Instead of just calculating the area of a standalone circle or square, students are challenged to find the area of complex, shaded regions formed when circles intersect with, or are contained within, triangles, rectangles, squares, or even other circles. Mastering this concept involves visualizing complex shapes as a composite of simpler, recognizable geometric figures that have been layered or cut out from one another.
The core logic to solving problems based on combinations lies in the straightforward principle of addition and subtraction of standard geometric areas. First, you must identify the distinct basic shapes within the complex figure. The general mathematical approach is: Area of Shaded Region = Area of Larger Figure - Area of Unshaded Figure(s) (or vice versa, depending on the combination). For example, if a circle is inscribed perfectly within a square and you are asked to find the area of the corner gaps, you calculate the Area of the Square (side²) and subtract the Area of the Circle (πr²). Careful attention to dimensions—such as deducing that a square's side ($a$) is exactly equal to an inscribed circle's diameter ($2r$)—is a crucial first step before applying any formulas.
The diagram above perfectly illustrates a classic combination problem commonly tested in CBSE Class 10 board exams. On the left side of the visual, we have a blue shaded square with an unshaded, white circle perfectly inscribed inside it. To find the area of the blue corners (the shaded region), the calculation steps on the right follow our core logic. We first determine the area of the outer boundary, which is the square with a side of 14 cm, yielding 196 cm². Next, we calculate the area of the inner unshaded boundary—the circle with a radius of 7 cm—giving 154 cm². By simply subtracting the circle's area from the square's area, we easily isolate the remaining space, revealing that the area of the four shaded corners is exactly 42 cm². This step-by-step extraction method is universally applicable to virtually any complex geometric combination, from overlapping semi-circles to sectors cut from triangles.
Mastering problems based on combinations of plane figures requires strong visualization skills and a solid grasp of how fundamental geometric formulas interact. If you are struggling to identify the right shapes to add or subtract, or need help tackling more complex textbook exercises, expert guidance can make a significant difference in your preparation. Discover highly experienced and verified CBSE Class 10 Mathematics tutors on UrbanPro. Whether you prefer interactive online sessions or localized offline tuition, UrbanPro connects you with the perfect tutor to help you confidently conquer 'Areas Related to Circles' and score higher in your board exams.
Other Concepts in Areas Related to Circles
Top Tutor 
Ashok Vihar, Gurgaon 
1 student 
214 hrs of classes completed 
350 per hour 
Online Classes With a strong academic foundation in Mathematics, including an M.Sc. in Mathematics, B.Sc., BTC, and CTET qualification, I am a dedicated Mathematics educator committed to helping students build conceptual clarity, logical reasoning, and analytical problem-solving skills. I have been successfully teaching Mathematics for over 12 years through my coaching institute in Gurgaon, while also conducting engaging online classes for students across India and internationally. I teach students across CBSE, ICSE, NIOS, and State Boards, adapting my teaching methodology to suit each curriculum and the individual learning needs of every student. My teaching approach focuses on simplifying complex mathematical concepts through structured lesson planning, personalised instruction, continuous assessment, and interactive learning techniques. I believe every student can excel in Mathematics with the right guidance, consistent practice, and a strong conceptual foundation. I also specialise in Vedic Mathematics, helping students significantly improve calculation speed, accuracy, mental agility, and confidence in school, competitive, and entrance examinations. As an UrbanPro Super Tutor, I am recognised for consistently delivering high-quality teaching and maintaining excellent student and parent satisfaction. Over the years, I have helped hundreds of students achieve outstanding academic results while developing confidence and a genuine interest in Mathematics. My passion for teaching, commitment to academic excellence, and student-centred approach enable me to create an engaging, motivating, and result-oriented learning environment where every learner can achieve their highest potential. If you are looking for a dedicated and experienced Mathematics tutor who can help you achieve excellent results and build strong fundamentals, I invite you to book a demo class today. Let’s work together to make Mathematics simple, enjoyable, and rewarding for you!
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Top Tutor Sector-18, Faridabad 5 students 1038 hrs of classes completed 600 per hour Online Classes I have approximately 3 years of experience of teaching Mathematics across different boards including CBSE, IGCSE and state board in reputed schools like DPS International. I am post graduate in statistics and honors degree in mathematics from reputed universities like DU. I have helped many students to overcome their fear of Mathematics and Statistics. My aim is to develop a genuine love for the subject in students.
The best math teacher my son has ever had! She explains every concept with clarity, makes learning enjoyable, and ensures he fully understands each topic. Truly inspiring and supportive.
Top Tutor Uttam Nagar, Delhi 5 students 312 hrs of classes completed 300 per hour Online Classes 
Tutor's home teach them with practical and theory base method
Top Tutor Electronic City Electronic City Phase II, Bangalore 4 students 38 hrs of classes completed 150 per hour Online Classes Tutor's home I was completed my m.Tech in engineering. I was maintained tuition center from 7 years in my home to all subjects from 1st grade to 10th grades across different boards including CBSE,ICSE,STATE BOARD (expert in math and physics) and I have 2 years experience in engineering college and i took classes for engineering students . My teaching style is create every student in to think and learn and convert every student in to passionate about their subjects. Over the years i helped to so many students to grown their career and overcome their fear about maths ,physics.
Super Tutor Kharghar Sector 27, Mumbai 30 students 1077 hrs of classes completed 650 per hour Online Classes 
Student's Home **Teaching Methodology:** My approach to teaching Mathematics and Science is personalized and interactive. I focus on understanding each student's unique learning style and adapt my methods accordingly. My goal is to make Maths and Science relatable and engaging, using real-life examples and practical applications to enhance understanding.I try to develop self thinking on problem and pushing them to solve by self **Key Skills:** - Strong grasp of Mathematics concepts across various levels - Ability to simplify complex topics for better understanding - Excellent communication and motivational skills - Patient and supportive, ensuring a comfortable learning environment - Regular progress assessments and constructive feedback **Services Offered:** - One-on-one personalized tutoring sessions - Homework and assignment assistance - Exam preparation and revision classes - Online and in-person tutoring options - Flexible scheduling to accommodate student needs **Achievements:** - Helped students improve their grades by an average of [25%] - Successfully prepared students for competitive exams with [JEE,NEET,IMO] - Received positive feedback and high ratings from students and parents Interested in improving your Maths AND Science skills? Contact me today to schedule a session and take the first step towards mastering Mathematics and Science!
This teacher is incredibly friendly and teaches in a very calm and patient manner. He helped me clear all my doubts; after failing my board exams previously, I managed to score 47/80 in Mathematics under his guidance. He truly excels at building a student's confidence.
It refers to a specific mathematical method or property in Areas Related to Circles used to solve problems involving Problems based on combinations.
This concept is crucial for the exams as questions related to Areas Related to Circles and specifically Problems based on combinations are very common. It helps secure marks in the section effectively.
Yes, Problems based on combinations is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Areas Related to Circles chapter.
Students often miss the minute details or fundamental definitions of Problems based on combinations. Regular revision and practice are needed to master the nuances.
Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.
UrbanPro connects you with experienced Mathematics tutors who can explain Problems based on combinations with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.
