Understand the rule first
Perimeter measures the boundary, area measures a flat surface and volume measures three-dimensional space. Compound shapes can be split into rectangles without overlap.
Perimeter, area & volume 11+ practice
Distinguish perimeter, area and volume and calculate each with correct units.
A rectangle is 9 cm by 4 cm. Find its perimeter and area.
- Perimeter: 2 × (9 + 4) = 26 cm.
- Area: 9 × 4 = 36 cm².
- Boundary uses cm; surface uses cm².
A common misconception
Using the same formula or units for perimeter, area and volume.
Reusable method: Write the required measure and units before choosing a formula.Question 1 of 10 MathscoreA square has area 81 cm². What is its perimeter?
- A36 cm
- B18 cm
- C40 cm
- D324 cm
Need a hint?
Find the side length whose square is 81.
Show worked answer
Answer A: 36 cm
The side is 9 cm, so the perimeter is 4 × 9 = 36 cm.
Quick method: Write the required measure and units before choosing a formula.
Question 2 of 10 MathscoreA triangle has base 12 cm and perpendicular height 7 cm. What is its area?
- A19 cm²
- B42 cm²
- C84 cm²
- D38 cm²
Need a hint?
Use one half × base × perpendicular height.
Show worked answer
Answer B: 42 cm²
12 × 7 ÷ 2 = 42 cm².
Quick method: Write the required measure and units before choosing a formula.
Question 3 of 10 MathscoreA cuboid measures 6 cm by 4 cm by 3 cm. What is its volume?
- A13 cm³
- B24 cm³
- C72 cm³
- D78 cm³
Need a hint?
Multiply all three dimensions.
Show worked answer
Answer C: 72 cm³
6 × 4 × 3 = 72 cm³.
Quick method: Write the required measure and units before choosing a formula.
Question 4 of 10 Mathsexam-styleA 10 cm by 8 cm rectangle has a 3 cm by 2 cm rectangle cut from one corner. What area remains?
- A48 cm²
- B76 cm²
- C86 cm²
- D74 cm²
Need a hint?
Subtract the small rectangular area from the large one.
Show worked answer
Answer D: 74 cm²
10 × 8 − 3 × 2 = 80 − 6 = 74 cm².
Quick method: Write the required measure and units before choosing a formula.
Question 5 of 10 Mathsexam-styleA cube has edges of 5 cm. What is its volume?
- A125 cm³
- B25 cm³
- C20 cm³
- D150 cm³
Need a hint?
Multiply the edge length three times.
Show worked answer
Answer A: 125 cm³
5 × 5 × 5 = 125 cm³.
Quick method: Write the required measure and units before choosing a formula.
Question 6 of 10 MathscoreA rectangle is 8 cm long and 5 cm wide. What is its perimeter?
- A13 cm
- B40 cm
- C80 cm
- D26 cm
Need a hint?
Add two lengths and two widths.
Show worked answer
Answer D: 26 cm
Perimeter = 2 × (8 + 5) = 26 cm.
Quick method: Write the required measure and units before choosing a formula.
Question 7 of 10 MathscoreWhat is the area of a triangle with base 12 cm and perpendicular height 7 cm?
- A42 cm²
- B19 cm²
- C84 cm²
- D38 cm²
Need a hint?
Use one half × base × height.
Show worked answer
Answer A: 42 cm²
Area = 1/2 × 12 × 7 = 42 cm².
Quick method: Write the required measure and units before choosing a formula.
Question 8 of 10 MathscoreA cuboid measures 6 cm by 4 cm by 3 cm. What is its volume?
- A13 cm³
- B72 cm³
- C54 cm³
- D108 cm³
Need a hint?
Multiply all three dimensions.
Show worked answer
Answer B: 72 cm³
6 × 4 × 3 = 72 cm³.
Quick method: Write the required measure and units before choosing a formula.
Question 9 of 10 MathsexamAn L-shape is made from a 10 cm by 8 cm rectangle with a 4 cm by 3 cm rectangle removed. What is its area?
- A56 cm²
- B64 cm²
- C68 cm²
- D76 cm²
Need a hint?
Find the large area, then subtract the cut-out.
Show worked answer
Answer C: 68 cm²
10 × 8 = 80 cm² and 4 × 3 = 12 cm². The L-shape area is 80 − 12 = 68 cm².
Quick method: Write the required measure and units before choosing a formula.
Question 10 of 10 MathsstretchA cuboid has volume 360 cm³. Its base is 12 cm by 5 cm. What is its height?
- A3 cm
- B4 cm
- C5 cm
- D6 cm
Need a hint?
Divide the volume by the base area.
Show worked answer
Answer D: 6 cm
The base area is 12 × 5 = 60 cm². Height = 360 ÷ 60 = 6 cm.
Quick method: Write the required measure and units before choosing a formula.