41 P5.AP.JM.17083246
Level 3
The figure, not drawn to scale, is made up of two identical squares, X and Z and a rectangle Y. The ratio of the area X to the area of Y to the area of Z is 1 : 2 : 1. The ratio of the unshaded part of X to the unshaded part of Z is 2 : 3 respectively. Given that half of the area of X is shaded and the total area of all the shaded parts is 48 m2, what is the area of the whole figure?
3 m
Square Rectangle Rectilinear figure Composite figure area Overlapping area Ratio to units Units method
42 P5.AP.JM.17083247
Level 3
Two identical triangles, ABC and XYZ, overlap each other as shown. Given that AB = XY = 15 cm and BC = YZ = 14 cm, what is the area of the figure that is not shaded?
3 m
Triangle Overlapping area
43 P5.AP.JM.17083200
Level 3
The figure shows two identical right-angled triangles overlapping each other. Find the area of the shaded part.
3 m
Right-angled triangle Overlapping area
44 P5.AP.JM.17083245
Level 3
The figure is made up of 3 similar overlapping squares of side 6 cm. The squares touched one another at Corners A, B, C, D and E. Jim shaded the parts where the squares overlapped each other.
  1. Find the area of the unshaded part of the figure.
  2. What fraction of the figure is the shaded part?
3 m
Square Composite figure area Overlapping area Fraction of a whole
45 P4.AP.JM.17100269
Level 3
Two rectangles of length 14 cm and breadth 10 cm, are placed one on top of the other to form a shape as shown. What is the area of the shape?
3 m
Rectangle Overlapping area
46 P4.AP.JM.17100266
Level 3
X and Y are identical squares. X overlaps Y partially as shown. What is the area of the shaded part?
3 m
Square Overlapping area
47 P4.AP.JM.17100267
Level 3
The figure is made up of 2 identical rectangles partially overlapping each other. Find the perimeter of the figure.
3 m
Rectangle Overlapping area
48 P4.AP.JM.17100265
Level 3
Two identical squares overlap each other to form the figure shown. A and B are the centres of squares X and Y respectively. What fraction of the figure is shaded?
3 m
Square Overlapping area Fraction of a whole
49 P5.PC.JC.17083304
Level 3
The figure shows an irregular 5-sided figure and a square. The area of the five-sided figure was three times the area of the square. After the shaded part was removed, the area of the remaining square became 15% of the total remaining area of both figures. If the area of the shaded part is 16 cm2, find the remaining area of the 5-sided figure.
4 m
Area perimeter Overlapping area Percent to units Times as many Unchanged difference Units table
50 P4.AP.NK.23050845
Level 3
Two rectangular mats, each 4 m by 6 m are placed on the floor as shown. The mats overlap and the area of the floor covered by the overlap is 8.4 m2. Find the length of AB.
3 m
Length Rectangle Rectilinear figure Overlapping area
51 P4.AP.NK.23050843
Level 3
The area of a rectangular sheet of paper ABCD is 108 cm2. It is then folded at a corner as shown below in Figure 2. Given that AD = 9 cm and AE = 4 cm.
  1. Find the length of CD.
  2. Find the perimeter of the unshaded part AEBCD.
3 m
Rectangle Triangle Overlapping area Folded figure
52 P4.AP.JM.17100268
Level 3
A rectangular strip of ribbon is folded as shown. What is the area of the strip of ribbon before it is folded?
3 m
Square Rectangle Overlapping area Folded figure
53 P5.AP.JM.17083244
Level 3
The figure consists of two overlapping squares ABCD and DEFG. H is the 15 mark of the sides, AB and FG. Express the shaded area as a fraction of the total unshaded area. (Give your answer in the simplest form.)
4 m
Square Composite figure area Overlapping area Fraction of a whole Fraction to units Units method
54 P5.AP.JM.17083248
Level 3
The ratio of the area of Rectangle A to that of Rectangle B to that of Rectangle C is 5 : 4 : 3. 310 of Rectangle A and 16 of Rectangle C are shaded. The shaded area is 36 cm2. Find the total unshaded area of the figure.
4 m
Rectangle Rectilinear figure Overlapping area Fraction to units Ratio to units Units table
55 P5.AP.NK.23041257
Level 3
The figure shows overlapping a rectangle. Find the area of the shaded part.
4 m
Rectange Triangle Composite figure area Overlapping area
56 P4.AP.NK.23050838
Level 3
The figure, not drawn to scale, is made up of 3 squares, A, B and C. The length of one side of square A is twice the length of one side of square B. The length of one side of square B is twice the length of one side of square C. If the length of square B is 16 cm, find the area of the shaded parts of the figure.
4 m
Length Square Overlapping area Times as many
57 P4.AP.NK.23050842
Level 3
Figure A is a rectangular piece of paper measuring 36 cm by 20 cm. James folded the paper along the dotted line to form Figure B. What is the area of the shaded part of the paper?
4 m
Rectangle Triangle Overlapping area Folded figure
58 P6.AP.TL.17090841
Level 3
The figure is made up of a right-angled triangle ABC and two semicircles with AB and BC as their diameters respectively. The two semicircles and the line AC meet at D as shown. AB = 12 cm. BC = 16 cm and AC = 20 cm. (Take π = 3.14)
  1. Find the perimeter of the shaded region. Correct the answer to 2 decimal places.
  2. Find the area of the shaded region.
5 m
Right-angled triangle Circumference Semicircle Composite figure perimeter Composite figure area Overlapping area D Place values D Round off
59 P6.AP.TL.17090851
Level 3
In the figure, not drawn to scale, WXYZ is a rectangle with a length of 45 cm and a width of 22 cm. The area of the quadrilateral ABCD is 75 cm2. Find the ratio of the shaded area to the unshaded area.
5 m
Rectangle Triangle Composite figure area Overlapping area Finding ratio R Simplest form
60 P5.AP.JM.17083241
Level 3
In the figure, not drawn to scale, Triangle ABC and DEF are identical right-angled triangles. Find the unshaded area of the figure.
5 m
Right-angled triangle Overlapping area

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