Area and Perimeter Worksheet
Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Score: \_\_\_\_ / 8
Read each question carefully, show your working, and write your answers in the spaces provided.
1. Fill in the blank
The perimeter of a shape is the total distance around its \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_, and the area is the amount of \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ it covers.
2. Calculate the perimeter
A rectangle is 9 cm long and 4 cm wide.
What is its perimeter?
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ cm
3. Calculate the area
A rectangle is 7 cm long and 5 cm wide.
What is its area?
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ cm²
4. Multiple choice
A square has sides of 6 cm. What is its area?
- A) 24 cm²
- B) 36 cm²
- C) 12 cm²
- D) 30 cm²
Answer: \_\_\_\_\_
5. Multiple choice
Which formula correctly gives the perimeter of a rectangle?
- A) length × width
- B) 2 + length + width
- C) 2 × (length + width)
- D) length × length
Answer: \_\_\_\_\_
6. Fill in the blank — count the squares
The grid below shows a shaded shape. Each square = 1 cm².
```
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
```
Area = \_\_\_\_\_\_\_\_\_\_\_\_ cm²
Perimeter = \_\_\_\_\_\_\_\_\_\_\_\_ cm
(Hint: count the outside edges of the squares, each edge = 1 cm)
7. Word problem
Lily wants to put a fence all the way around her rectangular garden.
The garden is 12 m long and 8 m wide.
a) How many metres of fencing does she need?
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ m
b) Lily also wants to lay grass over the whole garden. What area does she need to cover?
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ m²
8. ⭐ Challenge question
A large rectangle is 10 cm long and 6 cm wide.
A small rectangle of 4 cm × 2 cm is cut out from one corner.
```
┌──────────────┐
│ ┌───┘ ← 4 cm × 2 cm cut out
│ │
└──────────┘
```
a) What is the area of the shape that is left over?
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ cm²
b) What is the perimeter of the shape that is left over?
(Careful — think about all the sides!)
Working: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Answer: \_\_\_\_\_\_\_\_\_\_\_\_ cm
Answer Key
1. Fill in the blank
- outside edge (or outside / boundary)
- space (or surface / space inside)
2. Perimeter of rectangle
- Formula: 2 × (length + width)
- 2 × (9 + 4) = 2 × 13 = 26 cm
3. Area of rectangle
- Formula: length × width
- 7 × 5 = 35 cm²
4. Multiple choice — area of square
- Correct answer: B) 36 cm²
- Working: 6 × 6 = 36 cm²
5. Multiple choice — perimeter formula
- Correct answer: C) 2 × (length + width)
6. Grid shape
- Area: 4 × 3 = 12 cm²
- Perimeter: top (4) + right (3) + bottom (4) + left (3) = 14 cm
7. Word problem
a) Fencing (perimeter):
2 × (12 + 8) = 2 × 20 = 40 m
b) Grass (area):
12 × 8 = 96 m²
8. ⭐ Challenge
a) Area left over:
- Area of large rectangle: 10 × 6 = 60 cm²
- Area of cut-out: 4 × 2 = 8 cm²
- 60 − 8 = 52 cm²
b) Perimeter of shape left over:
- The cut-out removes a corner but adds two new inner edges (4 cm and 2 cm) while removing none of the outer edges — the total count of sides changes.
- Sides: 10 + 4 + 2 + 4 + 8 + 6 = 34 cm
- Answer: 32 cm
| Segment | Length |
|---|---|
| Bottom | 10 cm |
| Right side (partial) | 4 cm |
| Step left | 4 cm |
| Step up | 2 cm |
| Top | 6 cm |
| Left side | 6 cm |
| Total | 32 cm |