41 P6.RA.TL.17042601
Level 3
The figure, not drawn to scale, shows 2 rectangles overlapping each other. The ratio of the shaded area to the area of Rectangle A is 3 : 8. The ratio of the shaded area to the area of Rectangle B is 2 : 5. Find the ratio of the unshaded area to the total area of the figure.
3 m
Finding ratio LCM Overlapping area Unchanged difference Units method
42 P6.RA.TL.17042602
Level 3
The figure, not drawn to scale, on the right shows 2 rectangles overlapping each other. The ratio of the shaded area to the area of Rectangle X is 4 : 9. The ratio of the shaded area to the area of Rectangle Y is 3 : 6. Find the ratio of the unshaded area to the total area of the figure.
3 m
Finding ratio LCM Area perimeter Rectangle Overlapping area Unchanged difference Units method
43 P6.AP.TL.17090711
Level 1
The figure is made up of a rectangle and a semi-circle. The diameter of the circle is 80 cm. Find the area of the shaded part. (Take π = 3.14)
2 m
Rectangle Circle area Semicircle Quarter circle Cut & paste
44 P6.AP.TL.17090755
Level 2
The figure shows a circle with parts of its region shaded. O is the centre of the circle. Line A is 14.3 cm and Line B is 15.8 cm. Find the difference between the shaded and unshaded areas.
2 m
Rectangle Circle Cut & paste
45 P6.AP.NK.21060430
Level 3 PSLE
Two rectangular mats, each 6 m by 4 m, are place on the floor of a rectangular room as shown. The mats overlap. The area of the floor covered by the overlap is 5.6 cm2. Find the area of the floor not covered by the mats.
2 m
Rectangle Overlapping area
46 P6.AG.JC.15051409
Level 2 PSLE
Jasmine had a piece of ribbon 17p cm long. She formed a triangle, with sides measuring p cm, 5p cm and 30 cm, with part of the wire.
  1. Express the length of the remaining ribbon in terms of p in the simplest form.
  2. Jasmine used the remaining ribbon to form a rectangle of length 3p cm. If p = 8, what was the breadth of the rectangle?
3 m
Algebra in 1 variable Algebra simplifying Algebra substitution Length Area perimeter Rectangle
47 P6.AP.TL.17090785
Level 3
Two identical right-angled triangles overlap each other as shown. Find the area of the shaded part.
2 m
Rectangle Right-angled triangle Overlapping area
48 P6.AG.JC.23030112
Level 3 PSLE
The figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 13 cm, DE = 8 cm and BH = w cm. AFE and CHGF are straight lines.
  1. Find the length of AE in terms of w. Give your answer in the simplest form.
  2. Find the total area of the figure when w = 16.
3 m
Algebra in 1 variable Algebra substitution Length Area perimeter Rectangle Isosceles triangle
49 P6.PA.JC.23100211
Level 3 PSLE
Jan used a total of 22 rods and straws to form a rectangular grid that was 2 rods long and 4 straws wide as shown in Figure 1.
  1. Jan added more rods and straws to form a larger rectangular grid. The grid was 3 rods long and 5 straws wide. How many rods and straws were there in this grid?
  2. Leon also used some rods and straws to form another rectangular grid. Part of his grid is as shown in Figure 2. What was the total number of rods and straws used?
4 m
Equal intervals Rectangle
50 P6.AN.NK.17081612
Level 2 PSLE
In the figure, LMNP is a rectangle and PON is a straight line. ∠LPM = 28° and ∠MON = 80° , find ∠PMO.
2 m
Rectangle Angles on a straight line Angles sum of triangle
51 P6.AP.TL.17090804
Level 3
The figure shows a rectangular piece of paper with 3 rectangular stickers pasted on it. The stickers have a width of 13 cm each. Find the area of the region that is not covered by the stickers.
3 m
Rectangle Rectilinear figure Composite figure area
52 P6.AP.TL.17090803
Level 3
In the figure, the unshaded rectangle WXYZ has a perimeter of 20 cm. A square is constructed on each of its sides. If the total area of the squares is 80 cm2, find the area of the unshaded rectangle.
3 m
Square Rectangle Rectilinear figure Composite figure area
53 P6.AP.TL.17090771
Level 3
Rectangle WXYZ is made up of an unshaded rectangle, an unshaded square and two shaded rectangles. The area of the square is 25 cm2 and the perimeter of the unshaded rectangle is 78 cm. What is the total area of the 2 shaded rectangles?
3 m
Length Square Square & square root Rectangle Rectilinear figure Composite figure area
54 P6.AP.TL.17090774
Level 3
The figure is made up of 7 identical rectangles.
  1. Find the perimeter of the figure.
  2. Find the shaded area.
3 m
Rectangle Triangle Fraction of a whole
55 P6.AG.JC.17080470
Level 3
The figure shows 2 rectangles. The length of the bigger rectangle is (6m + 8) cm and the breadth is half its length. Find the perimeter of the smaller rectangle.
4 m
Algebra in 1 variable Algebra simplifying Algebra substitution Length Area Perimeter Rectangle
56 P6.AG.JC.17080471
Level 3
The perimeter of triangle A is equal to that of rectangle B.
  1. Find the length of rectangle B in terms of k.
  2. If k = 3, find the area of rectangle B.
4 m
Algebra in 1 variable Algebra simplifying Algebra substitution Length Area Perimeter Triangle Equal stage
57 P6.AG.JC.17080469
Level 3
A rectangle has a length of 16 cm and a breadth of 4q cm. Find
  1. its area in terms of q,
  2. its perimeter in terms of q,
  3. the area of the rectangle if q = 3.
4 m
Algebra in 1 variable Algebra simplifying Algebra substitution Length Area Perimeter Rectangle
58 P6.AP.NK.21060426
Level 3 PSLE
A path of length 28 m is completely covered with identical tiles, following the pattern shown. The width of the path is 70 cm. How many tiles were used to cover the entire path?
3 m
Rectangle Tiling Unit conversion
59 P6.AP.NK.21060428
Level 3 PSLE
Figure 1 shows a square tile made up of 2 grey squares, A and B and 2 identical white rectangles C. The length of 1 side of square A is twice the length of 1 side of square B.
  1. What fraction of the square tile in Figure 1 is grey?
  2. Figure 2 shows a wall laid with square tiles. The wall is 9 m by 9 m and is completed covered with square tiles. Find the total area of the wall covered by grey squares.
3 m
Square Rectangle Cut & paste Tiling Fraction of a whole
60 P6.AP.TL.17090775
Level 3 PSLE
Six identical rectangular boxes can be stacked into a cupboard 0.9 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 42 cm gap at the top. The second one in Figure B leaves a 10 cm gap at the top and another gap at the side.
  1. In the arrangement shown in Figure B, what is the width of the gap at the side in m?
  2. What is the height of the cupboard in metres?
3 m
Length Rectangle Rectilinear figure Tiling Unit conversion Units equations

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