b × h: Challenge & Extension
Mathematics
GCSE Higher
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A challenging worksheet exploring the calculation of area for parallelograms using the formula b × h, incorporating practice, problem solving, real-world contexts, and extension questions.
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b × h: Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the area of a parallelogram with base 12 cm and height 7 cm.
[2 marks]2.
A parallelogram has a base of 15 m and an area of 135 m². Find its height.
[3 marks]3.
Construct a parallelogram on the grid with a base of 8 units and a height of 4 units. Calculate its area.
[3 marks]4.
A parallelogram has a base of 10 cm and an area of 80 cm². What is its height?
[3 marks]5.
A parallelogram with base 18 m has a height of 5 m. What is its area?
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems, showing detailed working.
1.
A gardener is designing a rectangular flowerbed with a parallelogram shape. The base is 20 meters long, and the height is 3 meters. The gardener decides to increase the height by 2 meters. What will be the new area, and by how much has it increased?
[4 marks]2.
A parallelogram has a base of 14 cm. Its area is 98 cm². If the height is reduced by 2 cm, what is the new area? Is the new area larger or smaller?
[4 marks]C
Real-world Applications
Solve these contextual problems involving b × h.
1.
A construction worker is laying bricks in the shape of a parallelogram with a base of 2 meters and a height of 0.5 meters. How many square meters of surface area do these bricks cover if they are arranged in a single layer?
[3 marks]2.
A farmer wants to fence a parallelogram-shaped field with a base of 250 meters and a height of 180 meters. Calculate the area of the field in hectares.
[3 marks]D
Challenge & Extension
Attempt these advanced problems that deepen your understanding of b × h.
1.
A parallelogram has a base of 9 units and an area of 54 square units. If the base is increased by 3 units, and the height remains the same, what is the new area? Explain your reasoning.
[4 marks]2.
Construct a parallelogram on the grid with a base of 7 units and a height of 3 units. Then, draw a line parallel to the base that divides the parallelogram into two smaller parallelograms with equal areas. Calculate the area of each smaller parallelogram.
[4 marks]E
Mixed Review & Error Analysis
Solve these questions and identify common errors.
1.
A student calculates the area of a parallelogram with base 10 cm and height 5 cm as 50 cm². However, they mistakenly use the base as the height and vice versa, calculating 5 × 10 = 50 cm². Is their calculation correct? Explain the mistake and correct it if necessary.
[3 marks]2.
A parallelogram has a base of 8 units and an area of 48 square units. A student mistakenly assumes the height is 8 units and calculates the area as 8 × 8 = 64. Identify the mistake and find the correct height.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet