Shape and space · Ages 9–10
Quadrilaterals, tiling and the eight directions worksheet
Covers: The rhombus, How quadrilaterals are related, Cutting up and putting together, The eight compass points, Measuring angles in degrees, Regular polygons and tiling, Drawing in one stroke
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Quadrilaterals, tiling and the eight directions worksheet
Shape and space · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A regular 7-sided shape is cut along lines from its centre. How many triangles do you get?
Answer:
2.A protractor measures ∠AOB. How many degrees is ∠AOB?
Answer:
3.The angles in the picture are all round one point. What is the angle marked ? in degrees?
Answer:
4.A regular polygon with 5 sides has sides 10 cm long. What is its perimeter in cm?
Answer:
5.At least how many lines (each joining two points) must be added so the drawing can be done in one stroke?
Answer:
Part B: Choose, or true or false (2 marks each)
6.Which shape is a rhombus?
- A
- B
- C
- D
Choose the right picture
Answer:
7.The picture shows rhombus ABCD. Which side is parallel to AB?
- A. BC
- B. AC
- C. DC
- D. AD
Choose the right answer
Answer:
8.Which shape is NOT a parallelogram?
- A
- B
- C
- D
Choose the right picture
Answer:
9.Which sentence is true?
- A. Every rectangle is a square
- B. Every rhombus is a square
- C. Every square is a rectangle
- D. Every parallelogram is a rectangle
Choose the right answer
Answer:
10.Cutting the shape along the lines in the picture, what shape is each piece?
- A. A four-sided shape
- B. A pentagon
- C. A hexagon
- D. A triangle
Choose the right answer
Answer:
11.North is at the top of the map. In which direction is 🐰 from 🐱?
- A. north-east
- B. south-west
- C. east
- D. north
Choose the right answer
Answer:
12.Ka-yee walks 4 steps north from the start, then 4 steps west. In which direction from the start is Ka-yee now?
- A. north-west
- B. south-east
- C. west
- D. north
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A rhombus-shaped flower bed has sides of 24 m. How many metres of fence go all round it?
Working:
Answer:
14.Ka-lok makes 4 rectangles (not squares) and 8 squares with sticks. How many of them are rhombuses?
Working:
Answer:
15.Ka-yee has 44 equal equilateral-triangle cards. Every 6 make a regular hexagon. At most how many hexagons can Ka-yee make?
Working:
Answer:
16.Ka-yan leaves home, walks 550 m north, then 550 m east, and reaches the library. In which direction is the library from home?
- A. north
- B. south-west
- C. east
- D. north-east
Choose the right answer
Working:
Answer:
17.Square tiles cover a square platform exactly, 9 along each side. How many tiles are in the outermost ring?
Working:
Answer:
18.The park's paths are shown. Ka-lok wants to walk every path exactly once. Which junction should Ka-lok start from?
- A. Junction 2
- B. Junction 1
- C. Junction 3
- D. Junction 4
Choose the right answer
Working:
Answer:
Show the answers and working
Quadrilaterals, tiling and the eight directions worksheet: Answers and working
Part A: Working out and filling in
1. 7 triangles
The centre is joined to every corner. Think how many triangles each side gets.
The centre joins every corner, so each side gets a triangle: 7.
2. 130°
First see which 0° OA lies on, then decide whether to read the inner ring or the outer one.
OA is on the 0° at the right, so read the inner ring: OB points at 130, ∠AOB = 130°.
3. 95°
Angles round a point make 360°. Add the three angles you already know first.
Add the known angles: 115 + 105 + 45 = 265; round a point is 360°: 360 − 265 = 95.
4. 50 cm
It has 5 sides, each 10 cm. The perimeter is all the sides added up.
A regular polygon's 5 sides are all the same length: 5 × 10 = 50.
5. 0 lines
First count the odd points. Then think what one new line joining two odd points does to them.
There are 0 odd points; each line joining two of them removes 2, until 2 or fewer remain: 0.
Part B: Choose, or true or false
6. D
Look at each shape in turn: are all four sides the same length?
A rhombus has four equal sides and both pairs of opposite sides parallel.
7. C. DC
A side that meets AB can't be parallel to it. See which sides share a corner with AB.
A rhombus's opposite sides are parallel: the side opposite AB is DC.
8. D
Check each shape: are both pairs of opposite sides parallel?
A trapezium has only one pair of parallel sides, so it isn't a parallelogram.
9. C. Every square is a rectangle
For each sentence, try to find a shape that breaks it. If you can, the sentence isn't true.
A square has four right angles and parallel opposite sides, so it is always a rectangle; not the other way round.
10. D. A triangle
Look at one piece first and count its sides.
Count each piece's sides: every piece has 3.
11. A. north-east
Stand at 🐱. Is 🐰 above or below it? To the left or the right?
Stand at 🐱 and look at 🐰: it is to the north-east.
12. A. north-west
Sketch it: 4 steps north, then 4 steps west. See which side of the start you end up.
As many steps north as west, so it ends between them: north-west.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 96 m
The fence goes all the way round, so it is the perimeter. All four sides are 24 m.
A rhombus's four sides are equal: 24 × 4 = 96.
14. 8 shapes
Think: does a rectangle that isn't a square have four equal sides? Does a square?
A square has four equal sides, so it is a rhombus; the other rectangles aren't: 8.
15. 7 hexagons
Every 6 make one. How many 6s are there in 44? Leftovers too few for a whole hexagon don't count.
44 ÷ 6 gives 7; what's left isn't enough for another.
16. D. north-east
Sketch it: 550 m north, then 550 m east. See which side of home the library is.
The two walks are equally long, so the library lies between north and east: north-east.
17. 32 tiles
Count 9 tiles along each of the four sides, then ask whether the corner tiles got counted twice.
Four sides of 9 each, but the four corner tiles are counted twice: 4 × 9 − 4 = 32.
18. A. Junction 2
Count the paths at each junction and find the odd junctions.
With two odd junctions, start at one of them: junction 2.
Numsprite · numsprite.com/en/worksheets/quadrilaterals-tiling-and-compass-points
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