NCERT Class 10 Maths — Chapter 11

Exercise 11.3: Combined Figures

Find the area of shaded regions in combined figures — circles inside squares, overlapping sectors, flower petal designs. These are the trickiest and most rewarding problems.

combined figuresshaded regionarea of combination
16
NCERT Questions
10
Practice MCQs
3
Key Concepts
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Extra Practice Questions

These questions cover the same concepts as Exercise 11.3. Try solving them to build confidence before or after the textbook exercise.

1

If the radius of a sector remains constant, but its central angle is doubled, then its area will ________.

A.double
B.quadruple
C.remain the same
D.be halved
2

Which of the following statements correctly defines a 'sector' of a circle?

A.The region enclosed by an arc and its corresponding chord.
B.The region enclosed by two radii and a diameter.
C.The region enclosed by two radii and their corresponding arc.
D.The region enclosed by two chords and an arc.
3

Consider a major sector of a circle with radius 'r' and minor angle 'θ'. Which of the following is a valid method to find the area of the major sector?

A.Calculate (θ/360°) × πr² and subtract this from the area of the full circle.
B.Calculate ((360° - θ)/360°) × πr².
C.Calculate the area of the minor sector and multiply it by 2.
D.Calculate the area of the full circle and divide it by 2.
4

If the area of a sector of a circle with radius 6 cm is 18π cm², what is the measure of the central angle of the sector?

A.180°
B.90°
C.120°
D.270°
5

Let ABC be a right-angled triangle with hypotenuse BC. Semi-circles are drawn externally on each side of the triangle as diameters. If the area of the semi-circle on AB is A1, on AC is A2, and on BC is A3, which of the following statements is always true?

A.A1 + A2 = A3
B.A1² + A2² = A3²
C.A1 + A2 > A3
D.A1 + A2 < A3
6

A square ABCD has a side length of 7 cm. A quadrant of a circle with center A and radius AD is drawn inside the square. What is the area of the shaded region, which is the part of the square *outside* the quadrant? (Use π = 22/7)

A.14 cm²
B.21 cm²
C.10.5 cm²
D.7 cm²
7

Two circles of radius 8 cm intersect each other such that each passes through the centre of the other. Find the area of the common region. (Use π = 3.14 and √3 = 1.73)

A.69.44 cm²
B.78.68 cm²
C.87.68 cm²
D.96.84 cm²
8

If a circle, a square, and an equilateral triangle all have the same perimeter 'P', which one encloses the maximum area?

A.The equilateral triangle
B.The square
C.The circle
D.The area is the same for all three.
9

A regular hexagon is inscribed in a circle of radius 'R'. Find the ratio of the area of the hexagon to the area of the circle.

A.3√3 / (2π)
B.3√3 / (π)
C.2√3 / (π)
D.√3 / (2π)
10

A square ABCD has side length 'a'. Four semi-circles are drawn *outwards* with each side of the square as diameter. Find the perimeter of the entire figure formed.

A.πa
B.2πa
C.πa/2
D.(π + 2)a
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Common Mistakes to Avoid

  • ✗Not breaking the figure into recognisable parts (circles, triangles, rectangles, sectors)
  • ✗Subtracting when you should add (or vice versa)
  • ✗Not identifying the correct dimensions from the figure

Other Exercises in Chapter 11

Exercise 11.1
Perimeter and Area of a Circle
Exercise 11.2
Area of Sector and Segment
Exercise 11.3
Combined Figures

Frequently Asked Questions

How many questions are in Exercise 11.3?

Exercise 11.3 has 16 questions on finding areas of combined and shaded figures.

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