Topics › KS3 › Geometry & measures

Perimeter & area

1. pa-01 Present from here

   What is the perimeter of this rectangle?

   
   A Option A: $22\text{ cm}$

   B Option B: $11\text{ cm}$

   C Option C: $24\text{ cm}$

   D Option D: $19\text{ cm}$
   Answer and misconceptions

   A Option A: $22\text{ cm}$ ✓ Correct

   B Option B: $11\text{ cm}$ ✗

   Adds only the labelled sidesCalculates 8 + 3, forgetting the two unlabelled sides.

   C Option C: $24\text{ cm}$ ✗

   Calculates the area insteadMultiplies 8 × 3, confusing perimeter with area.

   D Option D: $19\text{ cm}$ ✗

   Uses 2l + w instead of 2(l + w)Doubles only the length: 2 × 8 + 3 = 19, forgetting the width also appears twice.
2. pa-02 Present from here

   What is the area of this triangle?

   
   A Option A: $60\text{ cm}^2$

   B Option B: $35\text{ cm}^2$

   C Option C: $23\text{ cm}^2$

   D Option D: $30\text{ cm}^2$
   Answer and misconceptions

   A Option A: $60\text{ cm}^2$ ✗

   Forgets to halve base × heightCalculates 10 × 6, the area of the surrounding rectangle.

   B Option B: $35\text{ cm}^2$ ✗

   Uses the sloping side as the heightCalculates ½ × 10 × 7; the height must be perpendicular to the base.

   C Option C: $23\text{ cm}^2$ ✗

   Adds the lengths for areaCalculates 10 + 7 + 6, confusing area with adding lengths.

   D Option D: $30\text{ cm}^2$ ✓ Correct
3. pa-03 Present from here

   What is the area of this parallelogram?

   
   A Option A: $45\text{ cm}^2$

   B Option B: $18\text{ cm}^2$

   C Option C: $36\text{ cm}^2$

   D Option D: $28\text{ cm}^2$
   Answer and misconceptions

   A Option A: $45\text{ cm}^2$ ✗

   Multiplies base by the sloping sideCalculates 9 × 5; the height must be the perpendicular distance, 4 cm.

   B Option B: $18\text{ cm}^2$ ✗

   Halves as if it were a triangleCalculates ½ × 9 × 4, using the triangle formula for a parallelogram.

   C Option C: $36\text{ cm}^2$ ✓ Correct

   D Option D: $28\text{ cm}^2$ ✗

   Calculates the perimeter insteadCalculates 9 + 5 + 9 + 5, confusing area with perimeter.
4. pa-04 Present from here

   What is the area of this trapezium?

   
   A Option A: $80\text{ cm}^2$

   B Option B: $40\text{ cm}^2$

   C Option C: $300\text{ cm}^2$

   D Option D: $50\text{ cm}^2$
   Answer and misconceptions

   A Option A: $80\text{ cm}^2$ ✗

   Forgets to halve in the trapezium formulaCalculates (6 + 10) × 5 without multiplying by ½.

   B Option B: $40\text{ cm}^2$ ✓ Correct

   C Option C: $300\text{ cm}^2$ ✗

   Multiplies all the given lengthsCalculates 6 × 10 × 5, thinking area means multiplying every number.

   D Option D: $50\text{ cm}^2$ ✗

   Treats it as a rectangle using the longest sideCalculates 10 × 5, ignoring the shorter parallel side.
5. pa-05 Present from here

   All corners are right angles. What is the perimeter of this shape?

   
   A Option A: $27\text{ cm}$

   B Option B: $62\text{ cm}$

   C Option C: $33\text{ cm}$

   D Option D: $36\text{ cm}$
   Answer and misconceptions

   A Option A: $27\text{ cm}$ ✗

   Adds only the labelled sidesCalculates 10 + 8 + 4 + 5, missing the two unlabelled sides (6 cm and 3 cm).

   B Option B: $62\text{ cm}$ ✗

   Calculates the area insteadFinds 10 × 5 + 4 × 3 = 62, confusing perimeter with area.

   C Option C: $33\text{ cm}$ ✗

   Includes only one of the missing sidesAdds the inner 6 cm side but misses the inner 3 cm side.

   D Option D: $36\text{ cm}$ ✓ Correct