✕
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
Other Concept Videos for Problems based on combinations
Super Tutor 
Badarpur, Delhi 
143 students 
3519 hrs of classes completed 
200 per hour 
Online Classes 
Tutor's home
I am utterly grateful to Akshay sir for his unending support and sincere guidance. He was such a big pillar of support in my board exams and his style of teaching is truly exceptional!!!! His notes, his previous year questions, his tips and his advices are really helpful for the board exams. I was able to score 97.2% in my boards because of his style of teaching. In fact all the topics he marked as important came in the board exams! Moreover he is a very hardworking and dedicated teacher with an unending passion to support and tutor children. I really am grateful to you Akshay sir Regards Nirvaan Rai Batch 2025-26
Super Tutor Kodambakkam, Chennai 57 students 3670 hrs of classes completed 800 per hour Online Classes With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Super Tutor Nerul Sector 20, Thane 62 students 2785 hrs of classes completed 1200 per hour Online Classes I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level
He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.
Super Tutor Basaveshwara Nagar, Bangalore 11 students 3325 hrs of classes completed 500 per hour Online Classes With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!
Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!
Super Tutor Itagalpura Main Rd, Madappanahalli 133 students 3558 hrs of classes completed 600 per hour Online Classes I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classesX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.
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.
