📐 Area Explorer: Shapes, Surfaces & Spaces 🏗️

Area measures the space INSIDE a 2D shape. Surface area measures the total area of ALL faces of a 3D shape. Knowing these formulas lets you work out how much paint you need, how much carpet to buy, or how much wrapping paper to use for a gift!

▭ Rectangle
Area = length × width
A = l × w
Perimeter = 2(l + w)
🔺 Triangle
Area = ½ × base × height
A = ½bh
Height is PERPENDICULAR to base
◈ Parallelogram
Area = base × height
A = b × h
Height is perpendicular (not the slant!)

📋 Formula Reference

Rectangle

A = lw

Triangle

A = ½bh

Parallelogram

A = bh

Cuboid Surface Area

SA = 2(lw + lh + wh)

⭐ Golden Rules

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🔍 Worked Examples

Example 1: Area of a Rectangle

A bedroom floor is 4.5 m long and 3.2 m wide. Find the area.

📝 Formula: A = l × w
A = 4.5 × 3.2 = 14.4 m²
Also find perimeter: P = 2(l + w) = 2(4.5 + 3.2) = 2 × 7.7 = 15.4 m

Note: area is in m² (square metres), perimeter is in m (metres).

Example 2: Area of a Triangle

A triangle has base 8 cm and perpendicular height 5 cm. Find its area.

📝 Formula: A = ½ × b × h
A = ½ × 8 × 5 = 20 cm²
⚠️ Watch out: if the slant height was given (e.g., 6 cm), do NOT use it for area — always use the perpendicular height!

Example 3: Compound Shape (L-Shape)

An L-shaped room: total length 10 m, total width 8 m, with a rectangular section 4 m × 3 m cut from one corner. Find the area.

📝 Method: full rectangle − cut section
Full rectangle: 10 × 8 = 80 m²
Cut section: 4 × 3 = 12 m²
L-shape area: 80 − 12 = 68 m²

Example 4: Surface Area of a Cuboid

A box measures 6 cm × 4 cm × 3 cm. Find its surface area.

📝 Formula: SA = 2(lw + lh + wh)
= 2(6×4 + 6×3 + 4×3)
= 2(24 + 18 + 12)
= 2 × 54 = 108 cm²

A cuboid has 6 rectangular faces arranged in 3 identical pairs — that's where the × 2 comes from.

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🔬 Area Calculator

Choose a shape, enter the measurements, and see every working step!

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 1: Rectangle Area

A rectangle is 7 cm long and 4 cm wide. What is its area?

22cm²
28cm²
24cm²
32cm²

Drop the correct answer here:

Area =

💡 Hint: A = l × w = 7 × 4 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 2: Triangle Area

A triangle has base 10 cm and perpendicular height 6 cm. What is its area?

60cm²
20cm²
30cm²
40cm²

Drop the correct answer here:

Area =

💡 Hint: A = ½ × b × h = ½ × 10 × 6 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 3: Parallelogram Area

A parallelogram has base 9 cm and perpendicular height 5 cm. Find its area.

36cm²
40cm²
45cm²
54cm²

Drop the correct answer here:

Area =

💡 Hint: A = b × h = 9 × 5 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 4: Compound Shape

An L-shape is made by removing a 3 cm × 2 cm rectangle from a 8 cm × 6 cm rectangle. What is the area?

36cm²
42cm²
48cm²
54cm²

Drop the correct answer here:

Area =

💡 Hint: Full rectangle: 8 × 6 = 48. Remove: 3 × 2 = 6. Then 48 − 6 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 5: Surface Area of Cuboid

A cuboid measures 5 cm × 3 cm × 2 cm. What is its surface area?

58cm²
62cm²
66cm²
72cm²

Drop the correct answer here:

SA =

💡 Hint: SA = 2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6) = 2 × 31 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🎯 Drag Exercise 6: Find the Missing Dimension

A rectangle has area 56 cm² and width 7 cm. What is its length?

6cm
7cm
8cm
9cm

Drop the correct answer here:

Length =

💡 Hint: A = l × w, so l = A ÷ w = 56 ÷ 7 = ?

Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

✏️ Practice Questions

Work through all 20 questions. Click Show Answers when you're done!

  1. Find the area of a rectangle with length 9 cm and width 5 cm.
  2. Find the area of a rectangle with length 12 m and width 7 m.
  3. Find the area of a triangle with base 8 cm and perpendicular height 6 cm.
  4. Find the area of a triangle with base 15 m and perpendicular height 4 m.
  5. Find the area of a parallelogram with base 11 cm and perpendicular height 7 cm.
  6. Find the perimeter of a rectangle with length 8 m and width 3 m.
  7. A square has side 6 cm. Find (a) the area and (b) the perimeter.
  8. A triangle has base 14 cm and area 49 cm². Find the perpendicular height.
  9. A rectangle has area 72 cm² and length 9 cm. Find the width.
  10. Find the area of an L-shape made from an outer rectangle 12 cm × 8 cm with a 4 cm × 3 cm rectangle cut from one corner.
  11. Find the surface area of a cuboid measuring 10 cm × 5 cm × 4 cm.
  12. Find the surface area of a cube with side 6 cm.
  13. A floor is 5 m × 4.5 m. How many whole 1 m² tiles are needed to cover it completely?
  14. Find the area of a parallelogram with base 8 m and perpendicular height 4.5 m.
  15. Find the area of a triangle with base 20 cm and perpendicular height 9 cm.
  16. A rectangle has perimeter 32 cm and length 10 cm. Find its area.
  17. A room measures 7 m × 4 m. Carpet costs £12 per m². What is the total cost?
  18. Find the surface area of a cuboid measuring 8 cm × 3 cm × 5 cm.
  19. An L-shaped garden: large rectangle 10 m × 7 m, with a 3 m × 4 m rectangle removed from one corner. Find the area.
  20. A triangle has area 60 cm² and perpendicular height 10 cm. Find the base.

✅ Answers

  1. A = 9 × 5 = 45 cm²
  2. A = 12 × 7 = 84 m²
  3. A = ½ × 8 × 6 = 24 cm²
  4. A = ½ × 15 × 4 = 30 m²
  5. A = 11 × 7 = 77 cm²
  6. P = 2(8 + 3) = 2 × 11 = 22 m
  7. (a) A = 6 × 6 = 36 cm²  |  (b) P = 4 × 6 = 24 cm
  8. h = 2 × 49 ÷ 14 = 98 ÷ 14 = 7 cm
  9. w = 72 ÷ 9 = 8 cm
  10. Full rectangle: 12 × 8 = 96 cm². Cut: 4 × 3 = 12 cm². Area = 96 − 12 = 84 cm²
  11. SA = 2(10×5 + 10×4 + 5×4) = 2(50 + 40 + 20) = 2 × 110 = 220 cm²
  12. SA = 6 × (6²) = 6 × 36 = 216 cm²
  13. Area = 5 × 4.5 = 22.5 m². Need whole tiles, so 23 tiles
  14. A = 8 × 4.5 = 36 m²
  15. A = ½ × 20 × 9 = 90 cm²
  16. Perimeter = 32 cm, so 2(10 + w) = 32 → w = 6 cm. Area = 10 × 6 = 60 cm²
  17. Area = 7 × 4 = 28 m². Cost = 28 × £12 = £336
  18. SA = 2(8×3 + 8×5 + 3×5) = 2(24 + 40 + 15) = 2 × 79 = 158 cm²
  19. Large: 10 × 7 = 70 m². Remove: 3 × 4 = 12 m². Area = 70 − 12 = 58 m²
  20. b = 2 × 60 ÷ 10 = 120 ÷ 10 = 12 cm
Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area

🌟 Challenge Problems

10 trickier problems to stretch your thinking. Show all working!

  1. A garden measures 15 m × 12 m. A path 1 m wide runs around the INSIDE edge of the garden. What is the area of the path?
  2. A triangular sail has base 4 m and height 6.5 m. Find its area. If the material costs £8 per m², what is the total cost?
  3. A cuboid gift box measures 20 cm × 15 cm × 10 cm. How much wrapping paper (surface area) is needed?
  4. A square has the same area as a rectangle measuring 12 cm × 3 cm. What is the side length of the square?
  5. A parallelogram has area 84 cm² and base 12 cm. Find the perpendicular height.
  6. An L-shaped running track has overall outer dimensions 50 m × 30 m, with an inner rectangular cutout of 20 m × 15 m. What is the area of the track?
  7. A wall is 4.5 m × 3 m. One tin of paint covers 6 m². How many whole tins are needed to paint the wall?
  8. Two identical triangles are joined along their bases to form a parallelogram with base 8 cm and height 5 cm. Find the area of one triangle.
  9. A square room has perimeter 24 m. Find the area of the room.
  10. A cuboid has surface area 150 cm². Its length and width are both 5 cm. Find the height of the cuboid.

✅ Answers

  1. Outer area: 15 × 12 = 180 m². Inner garden (remove 1 m path on each side): 13 × 10 = 130 m². Path area = 180 − 130 = 50 m²
  2. Area = ½ × 4 × 6.5 = 13 m². Cost = 13 × £8 = £104
  3. SA = 2(20×15 + 20×10 + 15×10) = 2(300 + 200 + 150) = 2 × 650 = 1300 cm²
  4. Rectangle area = 12 × 3 = 36 cm². Side of square = √36 = 6 cm
  5. h = 84 ÷ 12 = 7 cm
  6. Outer area: 50 × 30 = 1500 m². Cutout: 20 × 15 = 300 m². Track area = 1500 − 300 = 1200 m²
  7. Wall area = 4.5 × 3 = 13.5 m². Tins needed = 13.5 ÷ 6 = 2.25 → need 3 tins (must round up)
  8. Parallelogram area = 8 × 5 = 40 cm². One triangle = 40 ÷ 2 = 20 cm²
  9. Side = 24 ÷ 4 = 6 m. Area = 6 × 6 = 36 m²
  10. SA = 2(lw + lh + wh) = 2(5×5 + 5×h + 5×h) = 2(25 + 10h) = 50 + 20h = 150. So 20h = 100, h = 5 cm. It's a cube!
Collins Stage 6 Cambridge Primary Maths · Unit 22: Area and Surface Area