81 P6.AN.NK.17050208
Level 3
In the figure, not drawn to scale, O is the centre of the circle. Given that the ratio of ∠OBC : ∠AOC is 3 : 11. Find ∠AOB.
4 m
Isosceles triangle Circle Angles at a point Ratio to units Units method
82 P6.AN.NK.17050211
Level 3
In the figure, not drawn to scale, O is the centre of the smaller circle. AB is a straight line. Find ∠AED.
4 m
Isosceles triangle Circle Angles on a straight line Alternate angles
83 P6.AP.TL.17090819
Level 3 PSLE
The figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 100 cm. The footpath is tiled using 38 circular tiles of diameter 50 cm, following the pattern shown. Each tile is in contact with those next to it.
  1. What is the area of the footpath not covered by the tiles? Take π = 3.14.
  2. What is the perimeter of the grass patch?
4 m
Square Rectangle Circle Area Tiling
84 P6.AP.TL.17090818
Level 3
The figure is not drawn to scale. Two balls, X and Y, turn and move along the line AB in opposite directions. The radius of X is 10 cm. The ratio of the diameter of Ball X to that of Ball Y is 5 : 2. If Ball X turns 10 rounds and Ball Y turns 2 rounds, how far apart are the centres of the balls? (Take π = 3.14)
4 m
Circle Circumference Ratio to units Distance apart
85 P6.AP.TL.17090820
Level 3
The figure shows 4 similar right-angled triangles arranged to form a big square which encloses a circle. The midpoints of the 4 sides of the big square touch the circumference of the circle. The two sides which form the right angle of each triangle are 16 cm and 12 cm respectively. Find the area of the shaded part. (Take π = 3.14)
4 m
Square Square & square root Right-angled triangle Circumference Circle area Composite figure area
86 P6.AP.NK.21060416
Level 2 PSLE
The outline of the shaded figure is formed by 3 identical small quarter circles, 2 identical large quarter circles and 3 straight lines. Take π = 3.14
  1. What is the radius of the large quarter circle?
  2. Find the perimeter of the shaded figure.
4 m
Length Quarter circle Composite figure perimeter
87 P6.AP.TL.17090824
Level 3
A piece of rope is used to make the figure shown. Inside the big semicircle are 2 small circles and 3 small semi-circles, all of which have the same radius. The diameter of the big semicircle is 30 cm. Find the area of the shaded region. (Leave the answer in terms of π)
4 m
Circle area Semicircle Composite figure area
88 P6.AP.TL.17090825
Level 3
The figure is made up of a circle, a triangle and a square of sides 28 cm. E is the mid-point of AD. Find the area of the shaded region. (Take π = 227)
4 m
Square Triangle Circle Composite figure area
89 P6.AP.TL.17090827
Level 3
Willi noticed the patterns on the square tiles and tried to calculate the area of the shaded part. Leave the answer in 2 decimal places. (Take π = 3.14)
4 m
Square Rectangle Quarter circle Composite figure area D Place values D Round off
90 P6.AN.NK.17050210
Level 3
In the figure not drawn to scale, O is the centre of the circle and RSU and PST are straight lines. If ∠TSU = 54° and ∠RSO is twice of ∠OSP, find ∠Q.
4 m
Isosceles triangle Circle Angles at a point Sum of angles in a quadrilateral Angles properties within a circle Times as many Units method
91 P6.AP.TL.17090828
Level 3
The figure shows a circle with centre O and diameter, 14 cm. ABCD and OAEB are squares. Find the total area of the shaded portions of the figure. (Take π = 227)
4 m
Square Triangle Circle area Composite figure area
92 P6.AP.TL.17090829
Level 3
The figure is made up of semicircles, a square, ABDF, and a rectangle, BCEF. The length of the square, ABDF, is 20 cm. Find the area of the shaded figure. Leave the answer in terms of π .
4 m
Square Rectangle Circle area Semicircle Composite figure area
93 P6.AP.TL.17090830
Level 3
The figure is made up of a quadrant, a square and a semicircle. The area of the square is 144 cm2. Find the area of the shaded parts. (Take π = 3.14)
4 m
Square Square & square root Circle area Semicircle Quarter circle Composite figure area
94 P6.AP.TL.17090831
Level 3
Find (a) the area and (b) the perimeter of the figure. (Take π = 227)
4 m
Circle area Composite figure perimeter Composite figure area
95 P6.AP.TL.17090832
Level 3
Find the:
  1. area and
  2. perimeter of the shaded part. The diameter of the small circle is 6 cm. (Take π = 3.14)
4 m
Circumference Circle area Composite figure perimeter Composite figure area
96 P6.AP.TL.17090833
Level 3
The figure is made up of identical quadrants. The radius is 10 cm long. Take π as 3.14.
  1. Find the area of the shaded part.
  2. Find the perimeter of the shaded part.
4 m
Circle area Quarter circle Composite figure perimeter Composite figure area
97 P6.AP.TL.17090834
Level 3 PSLE
OPQRS is part of a circle of radius 10 cm. OPR and OQS are quarter circles. The area of the shaded part OQR is 40 cm2 and the perimeter of the shaded part OQR is 30 cm. For each of the following, use the calculator value of π to find:
  1. the area of the figure OPQRS, correct to 2 decimal places,
  2. the perimeter of the figure OPQRS, correct to 1 decimal places.
4 m
Quarter circle Composite figure perimeter Composite figure area D Place values D Round off
98 P6.AP.TL.17090835
Level 3
The figure shows one big quadrant and two small semicircles. The radius of the big quadrant is 60 cm.
  1. Find the perimeter of the shaded figure. (Take π = 3.14)
  2. Find the shaded area of this figure. (Take π = 3.14)
4 m
Triangle Semicircle Quarter circle Composite figure perimeter Composite figure area
99 P6.AP.TL.17090836
Level 3
In the figure, WXYZ and XYML are squares. P and N are centres of square WXYZ and PQRS respectively. O is the centre of XY. If WL = 56 cm, take π = 227 and find
  1. the perimeter of the shaded region,
  2. the area of the shaded region.
4 m
Square Circumference Circle area Semicircle Composite figure perimeter Composite figure area
100 P6.AP.TL.17090837
Level 3
The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line B) is 12 cm.
  1. Find the area of the shaded part.
  2. Find the perimeter of the dotted line. (Take π = 3.14)
4 m
Circle area Semicircle Quarter circle Composite figure perimeter Composite figure area More than or less than

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