541 P6.PA.JC.17111325
Level 3
A series of patterns of shaded and unshaded small triangles is shown.
  1. Which pattern has 141 shaded triangles?
  2. Find the number of unshaded triangles in Pattern 40.
  3. Find the total number of triangles in Pattern 90.
5 m
Equal intervals Square numbers
542 P6.PA.JC.17111330
Level 3
Some patterns of shaded and unshaded small squares is shown. The unshaded squares are those which lie on the diagonals of the figure. By considering the number patterns,
  1. find the total number of squares in Figure 30,
  2. find the total number of shaded squares in Figure 50.
  3. what will be the figure number that will have 49 squares?
5 m
Repeated patterns Square numbers
543 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
544 P6.PA.JC.17111326
Level 3
The diagram shows 3 squares, the length of which are 1 cm, 2 cm and 3 cm respectively. Each square is made up of small squares which has a length of 1 cm and alternate squares are coloured grey and white.
  1. How many small grey squares are needed to create a square of side 11 cm?
  2. Find the length of the side of a square if 196 small grey and white squares are used to create it.
  3. Find the number of small white squares when a square of side 18 cm is created?
5 m
Equal intervals Square numbers Area Perimeter Square
545 P4.AN.JM.17092861
Level 3
The figure shows 2 squares JKLM and NJPQ. ∠LJN = 114°.
  1. Name the line that is parallel with JP.
  2. Find ∠RJP.
  3. Find ∠JRQ.
4 m
Square Exterior angle of a triangle Overlapping angles
546 P4.AN.JM.17092858
Level 3
The figure shows 2 squares ABCD and CEGF, and a rectangle HIJC. ∠DCF = 34° and ∠ECJ = 40°.
  1. Name the line that is perpendicular to FC.
  2. Find ∠BCH.
  3. Find ∠HKC.
4 m
Square Rectangle Angles sum of triangle Overlapping angles
547 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
548 P3.AP.JM.17102370
Level 3
A piece of paper had a length of 15 cm and breadth of 10 cm. Four identical squares with sides 2 cm were cut out from the corners as shown.
  1. What was the area of the paper before it was cut?
  2. What was the area of the paper after the four corners were cut?
4 m
Square Rectangle Composite figure area
549 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
550 P4.AN.JM.17092872
Level 3
The figure shows a piece of square paper ABCD folded at two of its corners A and C. ∠AED is 3 times as large as ∠ADE and ∠CDF is 6° smaller than ∠ADE. Find ∠ADC.
4 m
Square Angles sum of triangle Overlapping angles Model Comparison Model Times-as-many Units method

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