Subtracting: Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on subtracting areas within compound shapes, including procedural practice, real-world problems, and extension challenges for Grade 8 students.
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Full preview • 11 questions
Subtracting: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the area of the shaded region by subtracting the smaller rectangle from the larger rectangle: Lengths are 12 cm and 5 cm for the smaller rectangle, and 20 cm by 15 cm for the larger rectangle.
[3 marks]2.
Subtract the area of a square with side 8 cm from a rectangle measuring 25 cm by 10 cm to find the remaining area.
[3 marks]3.
A compound shape consists of a rectangle 18 cm by 10 cm and a smaller rectangle removed from one corner measuring 6 cm by 4 cm. Find the net area of the shape.
[4 marks]4.
A swimming pool measures 25 m in length and 10 m in width. An embedded rectangular spa measuring 4 m by 2 m is to be subtracted from the pool's area for planning purposes. What is the remaining area of the pool?
[4 marks]5.
Construct a rectangle with an area of 48 cm². Then subtract a square of side 4 cm. What is the remaining area?
[3 marks]B
Challenge & Extension
Attempt these higher-level problems involving subtraction of areas in complex shapes.
1.
A trapezium has bases of 12 cm and 8 cm, and a height of 5 cm. Inside it, a smaller trapezium with bases 4 cm and 2 cm, and the same height, is cut out. Calculate the remaining area.
[4 marks]2.
A garden is shaped like a large rectangle measuring 30 m by 20 m. A circular pond with a radius of 5 m is to be removed from the corner. Calculate the remaining garden area.
[4 marks]3.
A composite shape is made of a rectangle 14 cm by 10 cm with a right-angled triangle removed from one corner, where the triangle has legs of 4 cm and 6 cm. Find the total remaining area.
[4 marks]C
Mixed Review
Solve these questions that combine various subtraction tasks.
1.
Subtract the area of a circle with radius 3 cm from a square with side 8 cm. (Use π ≈ 3.14 for calculations.)
[4 marks]2.
A rectangular room measures 6 m by 4 m. A small rectangular area of 1.5 m by 2 m is partitioned off. Find the usable area of the room.
[3 marks]D
Error Analysis
Below is a common mistake when subtracting areas. Identify the mistake and correct it.
1.
A student calculates the area of a rectangle as 20 cm x 10 cm = 200 cm², then subtracts an inner rectangle of 5 cm x 4 cm (area 20 cm²), and reports the remaining area as 180 cm². Identify and correct the mistake.
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet