EduSahara™ Assignment
Name : Areas of Complex Shapes
Chapter : Tangents and Secants to a Circle
Grade : SSC Grade X
License : Non Commercial Use
Question 1
1.
In the given figure, a circle is inscribed touching the sides of an equilateral triangle of side 28 cm. Find the area of the shaded region
  • (i)
    130.15 sq.cm
  • (ii)
    152.15 sq.cm
  • (iii)
    158.15 sq.cm
  • (iv)
    107.15 sq.cm
  • (v)
    134.15 sq.cm
Question 2
2.
In the given figure, the circle circumscribes a rectangle with sides 19.00 cm and 17.00 cm. Find the area of the remaining portion other than the rectangle
  • (i)
    180.71 sq.cm
  • (ii)
    201.71 sq.cm
  • (iii)
    187.71 sq.cm
  • (iv)
    165.71 sq.cm
Question 3
3.
In the given figure, the radius of the circle is 10 cm. Find the area of the minor sector
  • (i)
    73.57 sq.cm
  • (ii)
    83.57 sq.cm
  • (iii)
    78.57 sq.cm
  • (iv)
    81.57 sq.cm
  • (v)
    75.57 sq.cm
Question 4
4.
In the given figure, the radius of the circle is 11 cm. Find the area of the major sector
  • (i)
    280.21 sq.cm
  • (ii)
    289.21 sq.cm
  • (iii)
    267.21 sq.cm
  • (iv)
    313.21 sq.cm
  • (v)
    285.21 sq.cm
Question 5
5.
In the given figure ,PQRS is the diameter of the circle of radius 12.00 cm and PQ = QR = RS. Find the area of the shaded region
  • (i)
    329.71 sq.cm
  • (ii)
    314.71 sq.cm
  • (iii)
    285.71 sq.cm
  • (iv)
    298.71 sq.cm
  • (v)
    301.71 sq.cm
Question 6
6.
In the given figure ,PQRS is the diameter of the circle of radius 7.50 cm and PQ = QR = RS. Find the perimeter of the shaded region
  • (i)
    44.14 cm
  • (ii)
    42.14 cm
  • (iii)
    50.14 cm
  • (iv)
    47.14 cm
  • (v)
    52.14 cm
Question 7
7.
In the given figure , ABCD is a trapezium. A quarter circle AEFD is removed from the trapezium. If AD = CD = 10 and EB = 5.5 , find the area of the remaining portion
  • (i)
    51.93 sq.cm
  • (ii)
    48.93 sq.cm
  • (iii)
    45.93 sq.cm
  • (iv)
    53.93 sq.cm
  • (v)
    43.93 sq.cm
Question 8
8.
In the given figure, ABCD is a square of side 17.00 cm . At the centre there is a circle with radius 4.25 cm and the same circle quadrants are at the four corners. Find the area of the shaded region.
  • (i)
    171.46 sq.cm
  • (ii)
    147.46 sq.cm
  • (iii)
    189.46 sq.cm
  • (iv)
    175.46 sq.cm
  • (v)
    193.46 sq.cm
Question 9
9.
In the given figure, ABCD is a square of side 10.00 cm . At the centre there is a circle with radius 2.50 cm and the same circle quadrants are at the four corners. Find the perimeter of the shaded region.
  • (i)
    51.43 cm
  • (ii)
    46.43 cm
  • (iii)
    48.43 cm
  • (iv)
    54.43 cm
  • (v)
    56.43 cm
Question 10
10.
In the given figure, ABCD is a square of side 10.00 cm and A, B, C, D are the centres of circular arcs, each of radius 5.00 cm. Find the area of the shaded region
  • (i)
    16.43 sq.cm
  • (ii)
    26.43 sq.cm
  • (iii)
    18.43 sq.cm
  • (iv)
    21.43 sq.cm
  • (v)
    24.43 sq.cm
Question 11
11.
In the given figure, ABCD is a square of side 7.00 cm and A, B, C, D are centres of circles which touch externally in pairs. Find the area of the shaded region
  • (i)
    164.50 sq.cm
  • (ii)
    161.50 sq.cm
  • (iii)
    186.50 sq.cm
  • (iv)
    168.50 sq.cm
  • (v)
    141.50 sq.cm
Question 12
12.
In the given figure, BC = 14 cm and AB = 8 cm. Find the area of the shaded region
  • (i)
    148.29 sq.cm
  • (ii)
    122.29 sq.cm
  • (iii)
    176.29 sq.cm
  • (iv)
    134.29 sq.cm
  • (v)
    161.29 sq.cm
Question 13
13.
In the given figure, BC = 11 cm and AB = 6 cm. Find the perimeter of the shaded region
  • (i)
    71.91 cm
  • (ii)
    68.91 cm
  • (iii)
    63.91 cm
  • (iv)
    65.91 cm
  • (v)
    73.91 cm
Question 14
14.
In the below figure, AB is the diameter of a circle with center O and OA = 12.00 cm . Find the area of the shaded region
  • (i)
    195.43 sq.cm
  • (ii)
    212.43 sq.cm
  • (iii)
    183.43 sq.cm
  • (iv)
    187.43 sq.cm
  • (v)
    219.43 sq.cm
Question 15
15.
In the below figure, two circles with centers O and A touch internally at B. If OB = 17.00 cm and OA = 10.2 cm, find the area of the unshaded region
  • (i)
    774.96 sq.cm
  • (ii)
    762.96 sq.cm
  • (iii)
    746.96 sq.cm
  • (iv)
    788.96 sq.cm
  • (v)
    744.96 sq.cm
Question 16
16.
In the below figure, BCPQ is a quadrant of a circle. BC = 18.00 cm and AB = 12 cm . Find the area of the shaded region
  • (i)
    123.57 sq.cm
  • (ii)
    158.57 sq.cm
  • (iii)
    146.57 sq.cm
  • (iv)
    130.57 sq.cm
  • (v)
    152.57 sq.cm
Question 17
17.
In the below figure, BCPA is a quadrant of a circle. BC = 15.00 cm and CQA is a semicircle with CA as the diameter. Find the area of the shaded region
  • (i)
    128.50 sq.cm
  • (ii)
    136.50 sq.cm
  • (iii)
    107.50 sq.cm
  • (iv)
    112.50 sq.cm
  • (v)
    89.50 sq.cm
Question 18
18.
In the given figure, d = 14.00 cm is the diameter of the semi-circles. Find the area of the shaded region
  • (i)
    323.00 sq.cm
  • (ii)
    294.00 sq.cm
  • (iii)
    280.00 sq.cm
  • (iv)
    308.00 sq.cm
  • (v)
    322.00 sq.cm
Question 19
19.
In the given figure, find the area of the shaded region
  • (i)
    776.71 sq.cm
  • (ii)
    745.71 sq.cm
  • (iii)
    763.71 sq.cm
  • (iv)
    769.71 sq.cm
Question 20
20.
The given figure consists of four small semi-circles of equal radii and two big semi-circles of equal radii. The radius of each big semi-circle is 10.00 cm which is the same as the diameter of the small semi-circle. Find the area of the shaded region
  • (i)
    314.29 sq.cm
  • (ii)
    307.29 sq.cm
  • (iii)
    327.29 sq.cm
  • (iv)
    320.29 sq.cm
  • (v)
    302.29 sq.cm
Question 21
21.
The given figure consists of two quarter circles each of radius 12.00 cm and four semi-circles each of radius 6.00 cm. Find the area of the shaded region
  • (i)
    226.29 sq.cm
  • (ii)
    239.29 sq.cm
  • (iii)
    223.29 sq.cm
  • (iv)
    202.29 sq.cm
  • (v)
    244.29 sq.cm
Question 22
22.
In the given figure, the width of the circular path is 6.00 m. Find the area of the shaded region
  • (i)
    559.86 sq.m
  • (ii)
    564.86 sq.m
  • (iii)
    528.86 sq.m
  • (iv)
    532.86 sq.m
  • (v)
    546.86 sq.m
Question 23
23.
Find the area of the shaded region
  • (i)
    20.93 sq.cm
  • (ii)
    25.93 sq.cm
  • (iii)
    30.93 sq.cm
  • (iv)
    22.93 sq.cm
  • (v)
    28.93 sq.cm
Question 24
24.
Find the area of the shaded region
  • (i)
    94.21 sq.cm
  • (ii)
    130.21 sq.cm
  • (iii)
    108.21 sq.cm
  • (iv)
    95.21 sq.cm
  • (v)
    121.21 sq.cm
Question 25
25.
Find the area of the shaded region
  • (i)
    123.43 sq.cm
  • (ii)
    107.43 sq.cm
  • (iii)
    136.43 sq.cm
  • (iv)
    119.43 sq.cm
  • (v)
    92.43 sq.cm
Question 26
26.
In the given figure, BC = 8.00 cm. Find the area of the shaded region
  • (i)
    777.29 sq.cm
  • (ii)
    760.29 sq.cm
  • (iii)
    738.29 sq.cm
  • (iv)
    726.29 sq.cm
  • (v)
    754.29 sq.cm
Question 27
27.
In the given figure, arcs of two concentric circles of radii 11.00 cm and 3.30 cm are drawn with center O. If ∠GOH = 60°, find the area of the shaded region
  • (i)
    52.68 sq.cm
  • (ii)
    54.68 sq.cm
  • (iii)
    62.68 sq.cm
  • (iv)
    60.68 sq.cm
  • (v)
    57.68 sq.cm
Question 28
28.
In the given figure △ABC is an equilateral triangle whose area is 62.35 sq.cm. With each vertex of the triangle as center, a circle is drawn with radius equal to half the length of the side of the triangle . Find the area of the shaded region
  • (i)
    6.78 sq.cm
  • (ii)
    5.78 sq.cm
  • (iii)
    3.78 sq.cm
  • (iv)
    4.78 sq.cm
  • (v)
    7.78 sq.cm
Question 29
29.
In the given figure, ABCD is a square with side 15.00 cm. Find the area of the shaded region
  • (i)
    128.57 sq.cm
  • (ii)
    133.57 sq.cm
  • (iii)
    115.57 sq.cm
  • (iv)
    120.57 sq.cm
  • (v)
    156.57 sq.cm
Question 30
30.
Find the area of the shaded region in the given figure common between the two quadrants of circles of radius 16.00 cm each
  • (i)
    160.29 sq.cm
  • (ii)
    130.29 sq.cm
  • (iii)
    118.29 sq.cm
  • (iv)
    146.29 sq.cm
  • (v)
    159.29 sq.cm
    Assignment Key

  •  1) (v)
  •  2) (iii)
  •  3) (iii)
  •  4) (v)
  •  5) (v)
  •  6) (iv)
  •  7) (ii)
  •  8) (iv)
  •  9) (i)
  •  10) (iv)
  •  11) (i)
  •  12) (i)
  •  13) (ii)
  •  14) (i)
  •  15) (ii)
  •  16) (iii)
  •  17) (iv)
  •  18) (iv)
  •  19) (iii)
  •  20) (i)
  •  21) (i)
  •  22) (v)
  •  23) (ii)
  •  24) (iii)
  •  25) (iv)
  •  26) (v)
  •  27) (v)
  •  28) (ii)
  •  29) (i)
  •  30) (iv)