Unit 7 · Class 7 IB MYP · MCQ Test
Area & Perimeter MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Area & Perimeter — MCQ Questions
1A rectangular swimming pool in a Berlin park has a length of 15.5 metres and a width of 8 metres. If a safety rope needs to be placed around the entire perimeter of the pool, what length of rope is required?
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Answer: 47 metres
Hint: Remember that the perimeter of a rectangle is the sum of all its sides, or 2 × (length + width).
Solution:
Identify the given dimensions: Length = 15.5 m, Width = 8 m.
Apply the perimeter formula for a rectangle: Perimeter = 2 × (Length + Width). — P = 2 × (15.5 + 8)
Calculate the sum of length and width: 15.5 + 8 = 23.5 m.
Multiply by 2: 2 × 23.5 = 47 m.
2A classroom floor in Sydney, Australia, is a rectangle with a length of 9.2 metres and a width of 7 metres. What is the area of the floor? (Give your answer in square metres)
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Answer: 64.4 m²
Hint: To find the area of a rectangle, you multiply its length by its width.
Solution:
Identify the given dimensions: Length = 9.2 m, Width = 7 m.
Apply the area formula for a rectangle: Area = Length × Width. — A = 9.2 × 7
Perform the multiplication: 9.2 × 7 = 64.4 m².
3Alex was asked to find the area of a square with a side length of 6 cm. He wrote down the following steps: Step 1: Area = side + side Step 2: Area = 6 cm + 6 cm Step 3: Area = 12 cm² Which statement correctly identifies Alex's mistake?
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Answer: Alex used the formula for perimeter instead of area in Step 1.
Hint: Recall the correct formula for the area of a square. Area involves multiplication of dimensions, not addition.
Solution:
Review the formula for the area of a square: Area = side × side (or side²).
Review the formula for the perimeter of a square: Perimeter = 4 × side (or side + side + side + side).
Alex's Step 1, 'Area = side + side', is the formula for calculating two sides of a square's perimeter, not its area.
Therefore, Alex made a mistake by using an incorrect formula for area.
4A triangular sail on a yacht has a base of 4 metres and a perpendicular height of 6.5 metres. What is the area of the sail?
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Answer: 13 m²
Hint: The area of a triangle is half the product of its base and its perpendicular height.
Solution:
Identify the given dimensions: Base (b) = 4 m, Perpendicular height (h) = 6.5 m.
Apply the area formula for a triangle: Area = 1/2 × base × height. — A = 1/2 × b × h
Substitute the values: A = 1/2 × 4 × 6.5.
Calculate the area: A = 2 × 6.5 = 13 m².
5Consider a metal plate shaped like an 'L' with the following dimensions: The outer rectangle has a length of 10 cm and a width of 8 cm. A smaller rectangular section, 6 cm long and 4 cm wide, is cut out from one corner. What is the perimeter of the 'L'-shaped plate?
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Answer: 36 cm
Hint: For an L-shaped figure, the perimeter is still the sum of all its outer edges. Notice that the total length and width remain the same as the original outer rectangle, even with the cut-out.
Solution:
Visualise the L-shape. The outer dimensions are 10 cm by 8 cm.
The cut-out is 6 cm by 4 cm from a corner. The perimeter of an L-shape formed by cutting a rectangle from a corner of a larger rectangle is equal to the perimeter of the original larger rectangle. This is because the two inner edges created by the cut are equal in length to the two segments they replaced on the outer edge.
Perimeter of the outer rectangle = 2 × (Length + Width). — P = 2 × (10 + 8)
Calculate: P = 2 × 18 = 36 cm.
6A parallelogram-shaped garden plot in the Netherlands has a base length of 12 metres and a perpendicular height of 5.5 metres. What is the area of this garden plot?
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Answer: 66 m²
Hint: The area of a parallelogram is found by multiplying its base by its perpendicular height.
Solution:
Identify the given dimensions: Base (b) = 12 m, Perpendicular height (h) = 5.5 m.
Apply the area formula for a parallelogram: Area = base × height. — A = b × h
Substitute the values: A = 12 × 5.5.
Calculate the area: A = 66 m².
7The largest Ferris wheel in a city measures 135 metres in diameter. Approximately what is the circumference of the wheel? (Use π ≈ 3.14)
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Answer: 423.9 metres
Hint: The circumference of a circle can be calculated using the formula C = π × diameter.
Solution:
Identify the given dimension: Diameter (d) = 135 m.
Recall the formula for circumference: C = π × d.
Substitute the values and use the given approximation for π: C ≈ 3.14 × 135.
Calculate the circumference: C ≈ 423.9 metres.
8A circular pizza has a radius of 15 cm. What is the area of the pizza? (Use π ≈ 3.14 and round to one decimal place)
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Answer: 706.5 cm²
Hint: The area of a circle is calculated using the formula A = π × radius².
Solution:
Identify the given dimension: Radius (r) = 15 cm.
Recall the formula for the area of a circle: A = π × r². — A = π × 15²
Calculate the square of the radius: 15² = 225.
Substitute the value and use the given approximation for π: A ≈ 3.14 × 225.
Calculate the area: A ≈ 706.5 cm².
9A road sign in Switzerland is shaped like a trapezium. Its parallel sides measure 60 cm and 90 cm, and the perpendicular distance between them (height) is 40 cm. What is the area of the sign?
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Answer: 3000 cm²
Hint: The area of a trapezium is found using the formula A = 1/2 × (sum of parallel sides) × height.
Solution:
Identify the given dimensions: Parallel sides (a, b) = 60 cm and 90 cm, Height (h) = 40 cm.
Apply the area formula for a trapezium: Area = 1/2 × (a + b) × h. — A = 1/2 × (60 + 90) × 40
Calculate the sum of the parallel sides: 60 + 90 = 150 cm.
Substitute and calculate: A = 1/2 × 150 × 40.
Perform the multiplication: A = 75 × 40 = 3000 cm².
10A park in Tokyo has a rectangular section measuring 20 metres by 15 metres. Inside this section, there is a square pond with side length 5 metres. What is the area of the grass (the rectangular section excluding the pond)?
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Answer: 275 m²
Hint: To find the area of the grass, calculate the area of the entire rectangular section and then subtract the area of the square pond.
Solution:
Calculate the area of the rectangular section: Area_rectangle = Length × Width. — Area_rectangle = 20 × 15 = 300 m²
Calculate the area of the square pond: Area_pond = Side × Side. — Area_pond = 5 × 5 = 25 m²
Subtract the area of the pond from the area of the rectangle to find the area of the grass: Area_grass = Area_rectangle - Area_pond. — Area_grass = 300 - 25
Perform the subtraction: Area_grass = 275 m².
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Tips for Area & Perimeter MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Area & Perimeter MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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