Area of triangles and compound shapes
At Level 1 you go beyond simple rectangles. You need to find the area of triangles and compound shapes (shapes made of two or more simpler shapes joined together).
Area of triangle = ½ × base × height
Compound shape: split into rectangles/triangles, find each area, then add
Compound shape: split into rectangles/triangles, find each area, then add
💡 Triangle height: The height must be perpendicular (at right angles) to the base — it is not always the slanted side.
Volume of cuboids
Volume measures how much 3D space an object occupies. For a cuboid (box shape), multiply length × width × height.
Volume of cuboid = length × width × height
Units: cm³ or m³
Units: cm³ or m³
1 litre
= 1,000 cm³
1 m³
= 1,000,000 cm³
l × w × h
Cuboid volume formula
Scale drawings and maps
A scale shows the relationship between a distance on paper and the real-life distance. A scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in real life.
Real distance = map distance × scale factor
Map distance = real distance ÷ scale factor
Map distance = real distance ÷ scale factor
💡 Check your units: Convert to the same unit before calculating. 1 km = 1,000 m = 100,000 cm.
Speed, distance and time
These three measures are linked by a key formula. You can rearrange it to find whichever one is missing.
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Distance = Speed × Time
Time = Distance ÷ Speed
mph
miles per hour
km/h
kilometres per hour
m/s
metres per second
💡 Units must match: If speed is in mph, distance must be in miles and time in hours. Convert minutes to hours (÷60) before using the formula.
1Area of a triangle
▼A triangular flower bed has a base of 8 m and a perpendicular height of 5 m. What is the area?
- 1Formula: Area = ½ × base × height
- 2½ × 8 × 5 = 20 m²
✅ Area = 20 m²
2Area of a compound shape
▼An L-shaped room has outer dimensions 8 m × 6 m, with a 3 m × 2 m rectangular section cut from one corner. What is the floor area?
- 1Area of full rectangle: 8 × 6 = 48 m²
- 2Area of cut-out section: 3 × 2 = 6 m²
- 3L-shape area: 48 − 6 = 42 m²
✅ Floor area = 42 m²
3Volume of a cuboid
▼A storage box is 60 cm long, 40 cm wide and 30 cm high. What is its volume in cm³ and in litres?
- 1Volume: 60 × 40 × 30 = 72,000 cm³
- 2Convert to litres: 72,000 ÷ 1,000 = 72 litres
✅ Volume = 72,000 cm³ = 72 litres
4Using a map scale
▼A map has a scale of 1:25,000. Two towns are 8 cm apart on the map. What is the real distance in km?
- 1Real distance in cm: 8 × 25,000 = 200,000 cm
- 2Convert to m: 200,000 ÷ 100 = 2,000 m
- 3Convert to km: 2,000 ÷ 1,000 = 2 km
✅ Real distance = 2 km
5Calculating speed
▼A car travels 135 miles in 2 hours 15 minutes. What is its average speed in mph?
- 1Convert time: 2 hrs 15 min = 2.25 hours (15÷60=0.25)
- 2Speed = Distance ÷ Time: 135 ÷ 2.25 = 60 mph
✅ Average speed = 60 mph
6Metric–imperial conversion
▼A recipe uses 1 pint of milk. Approximately how many ml is this? (1 pint ≈ 568 ml)
- 1Use the conversion: 1 pint ≈ 568 ml
- 2So 1 pint of milk ≈ 568 ml
- 3This is just over half a litre (500 ml).
✅ 1 pint ≈ 568 ml (just over half a litre)
Question 1
A triangle has base 12 cm and height 9 cm. What is its area?
Question 1 (corrected)
A triangle has base 10 m and perpendicular height 6 m. What is its area?
Question 2
A cuboid fish tank is 50 cm long, 25 cm wide and 30 cm deep. What is its volume in litres?
Question 2 (corrected)
A box is 40 cm × 20 cm × 15 cm. What is its volume in cm³?
Question 3
A map scale is 1:50,000. Two points are 6 cm apart on the map. What is the real distance in km?
Question 4
A cyclist travels 48 km in 3 hours. What is their average speed?
Question 5
A train travels at 80 mph. How far does it go in 1 hour 30 minutes?
Question 6
An L-shaped path has total outer dimensions 10 m × 8 m, with a 4 m × 3 m section removed from a corner. What is the area?
Question 7
A journey of 45 miles is made at 60 mph. How long does it take (in minutes)?