1. Measurement Test: Unit 5
What unit would you use to measure the dimensions of
a skating rink? Why?
I would use metres because I know that a metre is about as big as a
giant footstep. I know that if I walked across a skating rink’s
length and width, the amount of footsteps would not be too big to
imagine in my head. I know I wouldn’t pick centimetres because a
centimetre is about as wide as my pinky finger and I know that the
length and width of a skating rink are a lot bigger than the width of
my pinky finger.

2. I think I would use decametres because a skating rink would be very
long (about 30 by 100 metres). I know that a metre is one big step,
so a decametre would be 10 big steps. I think it would make sense
to use decametres because I know that a hockey/skating rink is more
than 10 big steps long and wide.

3. In what way is the measurement 5.60 cm like 5.6 cm?
How is it different?
I know that if I put the measurement 5.6 cm in a place value chart,
then it would show that there are 5 cm and 6 mm. If I put 5.60 cm
in a place value chart, then it would also show that there are 5 cm
and 6 mm. That is how they are the same.
The difference is that 5.60 cm is being more precise and measuring to
the nearest hundredth of a metre instead of just to the nearest tenth of
a metre (5.6 cm).

4. Draw a hexagon and a rectangle that have the same
perimeter as this triangle.
The triangle has a perimeter of 12cm because each side is 4cm long.
4cm + 4cm + 4 cm = 12cm
I know that the hexagon and the rectangle have to have a perimeter of 12cm.
Properties of a hexagon: 6 equal sides
12cm ÷ 6 = 2cm
2cm + 2cm + 2cm + 2cm + 2cm + 2cm= 12cm
Each side of the hexagon is 2cm long.
Properties of a rectangle: opposite sides are equal, 4 sides
Guess and check
4cm + 2cm + 4cm + 2cm = 12cm SKETCH
SKETCH

5. Draw a square with a perimeter that is 4cm less than the
perimeter of the triangle in Question D.
I know that all sides are equal in a square.
The perimeter is 4cm less than in question D, so 12cm – 4cm = 8cm.
I will divide the perimeter by 4 (four equal sides): 8cm ÷ 4 = 2cm
2cm + 2cm + 2cm + 2cm = 8cm SKETCH

6. A regular hexagon and an equilateral triangle each
have a perimeter of 60cm. What are the side lengths
of each shape?
I know that there are 3 equal sides in an equilateral triangle, so I know that
I have to divide 60 by 3 to get my side lengths.
60cm ÷ 3 = 20cm
20cm + 20cm + 20cm = 60cm SKETCH
The side lengths of the equilateral triangle are 20cm each.
I know that there are 6 equal sides in a regular hexagon, so I know that
I have to divide 60 by 6 to get my side lengths.
60cm ÷ 6 = 10cm
10cm + 10cm + 10cm + 10cm + 10cm + 10cm = 60cm SKETCH
The side lengths of the regular hexagon are 10 cm each.

7. G. A rectangular tablecloth is 2.5 m long. Trim is to be sewn
around the perimeter of the cloth, but there is not enough.
What decrease in width will make the perimeter 0.4cm shorter
if the length remains the same.
Rectangle: 4 sides, opposite sides are equal
I know that the length must stay the same. The decrease in width needs to make the perimeter 0.4m shorter. Since the shorter sides are equal, the
decrease must be the same.
0.4 m ÷ 2 = 0.2 m SKETCH
The shorter sides must decrease by 0.2m each, so that the perimeter
decreases by 0.4m.

8. H. The shorter side of a rectangle is 20cm. Decreasing
the longer side by 30 cm reduces the perimeter by one
half. How long are the longer sides of the original rectangle?
Explain your reasoning. A
Rectangle: opposite sides are equal
A = C and B = D
Sides B and D = 20cm each
Strategy: guess and check D B C
Try Side A Side C Side B Side D Perimeter
40 cm cm cm cm cm + 40 cm + 20 cm + 20 cm = 120 cm
If I decrease the longer side by 30 cm (sides A and C)
10 cm cm cm cm cm + 10 cm + 20 cm + 20 cm = 60 cm
120 cm ÷ 2 (half) = 60 cm
This guess works because the perimeter is half when the longer sides are decreased by 30 cm.

9. One side of an isosceles triangle is 15 cm shorter than the
other 2 sides. The perimeter is 120 cm. How long are the sides
of the triangle?
Isosceles triangle: 2 equal sides
A = B
Side C is 15cm shorter than A and B
Perimeter: A + B + C = 120cm
Guess and check
Try Side A Side B Side C ( 15 cm shorter) Perimeter
45cm cm cm (45 – 30) cm + 45cm + 30 cm = 120cm
Side A = 45cm, Side B = 45cm, and Side C= 30cm A B C

10. Which of the two shaded polygons has a smaller perimeter?
How do you know?
The shape on the left has the smaller perimeter because the shape does
not have many horizontal and vertical “cut outs”. More “cut outs” increase the
perimeter of a polygon.

11. Which of the two has a smaller area? How do you know?
The polygon on the right has a smaller area. It does not cover as much of
the rectangle as the polygon on the left.

12. Draw a polygon with a perimeter of 92 cm inside
a rectangle with a perimeter of 54 cm.