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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 
Pandeypur, Varanasi 
13 students 
1964 hrs of classes completed 
500 per hour 
Online Classes I am Mathematics teacher teaching in a reputed school.
Sir explains questions very well and solves my doubts patiently. Even if I have any problems with questions at any time of the day, he still attends to them. I am satisfied.
Top Tutor Sector-63 Mohali, Chandigarh 1 student 11 hrs of classes completed 500 per hour Online Classes 
Tutor's home I have been tutoring students from past 6 years and as a professional School teacher from past 4 years . I know what is the competition and how to make student competent to face that with effective learning material and concept clarity .
Excellent experience. Service was wonderful. There was ambience habitat. All the things was understand easily.
Top Tutor Paschim Vihar, Delhi 5 students 144 hrs of classes completed 400 per hour Online Classes 
Student's Home Tutor's home I am a home tutor and teaching physics & mathematics up to class 12 for last 8 years. I am NET 2018, GATE 2013 & GATE 2011 qualified. My highest qualification is MTECH. I am an engineering graduate.
Top Tutor Bicholi Mardana Neer Nagar, Indore 12 students 362 hrs of classes completed 900 per hour Online Classes I have Taught 3 years in CBSE board and 5 years In ICSE board in class 10 with 100% results.Got an opportunity to go for CBSE board class 10 Maths copy correction.Was Board examiner head for ICSE .
Pragya ma'am is amazing! She helped me with maths a lot! Great teacher!
Top Tutor Sikandra, Agra 1 student 350 per hour Online Classes Student's Home I can teach every topic very easily and make it stronger for the students.
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.
