Perimeter & Area – Grade 5 Maths

Perimeter

Total distance around a shape

Area of Rectangles

l × w = area

Area of Triangles

½ × base × height

Compound Shapes

Split into simpler shapes

Units of Area

cm², m², km²

1. Perimeter

The perimeter is the total distance around the outside of a shape. Add up all the side lengths.

Perimeter of rectangle = 2 × (length + width) = 2l + 2w

Rectangle with length 8 cm and width 5 cm:
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm

💡 For a regular polygon (all sides equal): Perimeter = number of sides × side length

2. Area of Rectangles and Squares

Area is the amount of space inside a shape. It is measured in square units (cm², m², mm²).

Area of rectangle = length × width | Area of square = side²

Rectangle: length = 9 cm, width = 4 cm
Area = 9 × 4 = 36 cm²

💡 You can count squares on a grid to find area. Each square = 1 unit².

3. Area of Triangles

A triangle is exactly half of a rectangle with the same base and height.

Area of triangle = ½ × base × height

Triangle with base = 10 cm, height = 6 cm:
Area = ½ × 10 × 6 = ½ × 60 = 30 cm²

💡 The height is the perpendicular height — straight up from the base at 90°. It may not be a side of the triangle!

4. Compound Shapes

A compound shape is made from two or more simple shapes joined together.

Method:
1. Split the shape into rectangles (and/or triangles)
2. Find the area of each part
3. Add (or subtract) the areas together

L-shaped room: split into two rectangles. Rectangle 1: 6×4=24 m². Rectangle 2: 3×2=6 m². Total = 30 m²

💡 For a shape with a hole, calculate total area then subtract the hole.

5. Units of Area

Unit	Used for	Conversion
mm²	Very small areas	1 cm² = 100 mm²
cm²	Small areas (notebook)	1 m² = 10,000 cm²
m²	Rooms, floors	1 km² = 1,000,000 m²
km²	Countries, large areas

💡 Always write the correct unit in your answer — 36 is meaningless, but 36 cm² is an area.

Example 1 — Rectangle Perimeter and Area

A rectangle has length 12 cm and width 7 cm. Find the perimeter and area.

Perimeter = 2 × (12 + 7) = 2 × 19 = 38 cm

Area = 12 × 7 = 84 cm²

Example 2 — Triangle Area

A triangle has base 14 cm and perpendicular height 9 cm.

Area = ½ × 14 × 9 = ½ × 126 = 63 cm²

Example 3 — Compound Shape

An L-shape: total width 10 m, total height 8 m, with a 4×3 m rectangular notch cut from the top-right corner.

Total rectangle: 10 × 8 = 80 m²

Notch removed: 4 × 3 = 12 m²

Area = 80 − 12 = 68 m²

Example 4 — Missing Side from Area

A rectangle has area 72 cm² and one side of length 8 cm. Find the other side.

Area = l × w → 72 = 8 × w

w = 72 ÷ 8 = 9 cm

📐 Rectangle Calculator

Length: Width:

🔺 Triangle Area Calculator

Base: Height:

Exercise 1 — Perimeter of Rectangles

1. Rectangle: l=6 cm, w=4 cm. Perimeter?

2. Rectangle: l=9 cm, w=3 cm. Perimeter?

3. Square: side=7 cm. Perimeter?

4. Rectangle: l=15 m, w=8 m. Perimeter?

5. Regular pentagon: side=6 cm. Perimeter?

6. Rectangle: perimeter=30 cm, length=9 cm. Width?

7. Square: perimeter=48 cm. Side length?

8. Rectangle: l=12 m, w=5 m. Perimeter?

9. Regular hexagon: side=9 cm. Perimeter?

10. Rectangle: perimeter=44 cm, width=7 cm. Length?

Exercise 2 — Area of Rectangles and Squares

1. Rectangle: l=7 cm, w=4 cm. Area?

2. Square: side=9 cm. Area?

3. Rectangle: l=12 m, w=5 m. Area?

4. Rectangle: l=8 cm, w=8 cm. Area?

5. Rectangle: area=35 cm², l=7 cm. Width?

6. Square: area=64 cm². Side length?

7. Rectangle: l=20 m, w=15 m. Area in m²?

8. Rectangle: area=108 cm², l=12 cm. Width?

9. Square: area=144 cm². Perimeter?

10. Rectangle: l=25 cm, w=14 cm. Area?

Exercise 3 — Area of Triangles

1. Triangle: base=8 cm, height=5 cm. Area?

2. Triangle: base=12 cm, height=7 cm. Area?

3. Triangle: base=10 m, height=4 m. Area?

4. Triangle: base=9 cm, height=6 cm. Area?

5. Triangle: base=20 cm, height=11 cm. Area?

6. Triangle: area=24 cm², base=8 cm. Height?

7. Triangle: area=45 m², height=9 m. Base?

8. Right triangle: legs are the base(6 cm) and height(8 cm). Area?

9. Triangle: base=15 cm, height=8 cm. Area?

10. Triangle: base=30 m, height=14 m. Area?

Exercise 4 — Compound Shapes

Split shapes into rectangles. All measurements in cm.

1. L-shape: 10×8 total, with a 4×3 notch removed. Area?

2. Two rectangles joined: 6×4 and 3×2. Total area?

3. Rectangle 10×6 with a 2×2 square hole. Area?

4. T-shape: top bar 10×2, vertical bar 3×4. Total area?

5. Rectangle 12×8 with triangle on top: base=12, height=5. Total area?

6. Two squares: 5×5 and 3×3. Total area?

7. Rectangle 15×6 with a 3×4 notch removed. Area?

8. Cross shape: horizontal bar 12×2, vertical bar 2×10. Area? (centre counted once)

9. Rectangle 20×10 with two 4×3 notches removed. Area?

10. Square 8×8 with a triangle (base=8, height=4) on top. Total area?

Exercise 5 — Mixed Word Problems

1. A room is 6 m long and 4 m wide. Carpet costs £12 per m². Total cost?

2. A field is 80 m by 60 m. Farmer walks around it once. Distance walked (m)?

3. Square garden has perimeter 52 m. What is its area?

4. Triangle: base 14 m, height 8 m. Area?

5. Rectangle: area 84 cm², perimeter 38 cm. If width=6, what is length?

6. Square tile: side 30 cm. How many tiles needed to cover 1 m² floor? (1 m = 100 cm)

7. Rectangular path surrounds a 10×6 m garden, 1 m wide. Area of path?

8. A flag is 90 cm by 60 cm. Area in cm²?

9. Two identical triangles: base 10 cm, height 6 cm each. Total area?

10. Rectangle: l=13 cm, w=9 cm. Area?

🏋️ Practice — 20 Questions

1. Rectangle: l=10, w=7. Area?

2. Rectangle: l=10, w=7. Perimeter?

3. Triangle: base=6, height=8. Area?

4. Square: side=11. Perimeter?

5. Rectangle: area=56, l=8. Width?

6. Triangle: base=18, height=5. Area?

7. Square: perimeter=60. Area?

8. Rectangle: l=14, w=9. Area?

9. L-shape: 8×5 total, 3×2 notch removed. Area?

10. Triangle: area=40, base=10. Height?

11. Rectangle: l=20, w=3. Perimeter?

12. Triangle: base=24, height=7. Area?

13. Square: area=49. Side length?

14. Rectangle: perimeter=70, l=22. Width?

15. Rectangle: l=16, w=12. Area?

16. Regular octagon: side=5. Perimeter?

17. Two rectangles: 5×4 and 6×3. Total area?

18. Triangle: base=9, height=10. Area?

19. Rectangle: l=7, w=7. Perimeter?

20. Triangle: area=75, height=15. Base?

🏆 Challenge — 8 Questions

1. A rectangle has perimeter 36 cm and its length is twice its width. Find the area.

2. A square and a rectangle have the same perimeter of 40 cm. The rectangle is 12 cm long. Which has greater area — enter 1 for square, 2 for rectangle.

3. A triangle has area 60 cm². Its height is 3 more than its base. Find the base. (Base and height are whole numbers)

4. A path 2 m wide surrounds a 15×10 m pool. What is the area of the path?

5. A room 8 m × 6 m has a square window cut-out 1 m × 1 m. Tiles cost £8/m². Total cost to tile the floor?

6. Three identical squares have total area 108 cm². What is the side length of each?

7. A rectangle's length is 5 more than its width. Area = 84 cm². Find the width.

8. A large rectangle (20×12) has 4 identical triangles (base=4, height=3) removed from corners. Area remaining?

📐 Perimeter & Area