Measurement — Practice
Every conversion is a multiplication by one. Write the unit you want on top, the unit you have on the bottom, and the wrong units cancel themselves.
What these questions cover
These questions use 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Base — The number being multiplied. In 53 the base is 5.
- Factor — A number that divides evenly into another.
- Parallel — Same slope, different intercept.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Height — The perpendicular distance from the base to the opposite corner.
Problem 1
Convert 5 feet to inches.
Worked answer
60
5 × 12 = 60 in
Problem 2
Convert 2.5 m to centimetres.
Worked answer
250
2.5 × 100 = 250 cm
Problem 3
Find the perimeter of a 7 cm by 4 cm rectangle.
Worked answer
22
2(7 + 4) = 22 cm
Problem 4
Convert 3 km to metres.
Worked answer
3000
3 × 1000 = 3000 m
Problem 5
Find the area of a 6 m by 9 m rectangle.
Worked answer
54
6 × 9 = 54 m2
Problem 6
Convert 3 miles to feet. (1 mile = 5280 ft.)
Worked answer
15840
3 × 5280 = 15,840 ft
Problem 7
Convert 4500 mm to metres.
Worked answer
4.5
4500 ÷ 1000 = 4.5 m
Problem 8
Find the area of a triangle with base 14 and perpendicular height 9.
Worked answer
63
12(14)(9) = 63
Problem 9
A trapezoid has parallel sides 6 and 10 and height 5. Find its area.
Worked answer
40
6 + 102 = 8
8 × 5 = 40
Problem 10
How many square centimetres are in 1 square metre?
Worked answer
10000
1 m2 is 100 cm × 100 cm
= 10,000 cm2
Problem 11
A rectangle has perimeter 36 and length 11. Find its width.
Worked answer
7
22 + 2w = 36
2w = 14, so w = 7
Problem 12
Convert 2.5 hours to minutes.
Worked answer
150
2.5 × 60 = 150 min
Problem 13
Convert 12 m2 to square centimetres.
Worked answer
120000
1 m2 = 10,000 cm2
12 × 10,000 = 120,000 cm2
Problem 14
Convert 3 miles to inches. (1 mi = 5280 ft, 1 ft = 12 in.)
Worked answer
190080
3 × 5280 = 15,840 ft
15,840 × 12 = 190,080 in
Problem 15
An L-shape is a 10 × 8 rectangle with a 4 × 3 rectangle cut from one corner. Find its area.
Worked answer
68
10 × 8 = 80
4 × 3 = 12
80 - 12 = 68
Problem 16
A room is 4.5 m by 3.2 m. Carpet costs $28 per square metre. Find the total cost.
Worked answer
403.20
4.5 × 3.2 = 14.4 m2
14.4 × 28 = 403.20