Breaking Down: Challenge & Extension
Mathematics
Grade 8
10 questions
~20 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on breaking down complex shapes into simpler components to find their total area. It emphasizes understanding how to decompose shapes and apply area formulas effectively.
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Breaking Down: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Date:
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Untitled Worksheet
Grade Grade 8
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
A rectangle measures 8 cm by 3 cm. A smaller rectangle of 4 cm by 2 cm is cut out from the larger rectangle. Calculate the remaining area.
[3 marks]2.
A compound shape consists of a large square (10 cm sides) with a smaller rectangle (4 cm by 6 cm) attached to one side. Break down the shape into simpler parts to find its total area.
[4 marks]3.
A L-shaped figure is formed by combining two rectangles: one 8 cm by 4 cm and the other 6 cm by 3 cm. The rectangles share a 2 cm segment. Find the total area of the L-shape by breaking it down.
[3 marks]4.
Construct a shape consisting of a rectangle (9 cm by 5 cm) with a semicircular extension of radius 2.5 cm on one side. Calculate the total area, decomposing the shape into basic parts.
[4 marks]5.
A composite shape is made up of a rectangle (12 cm by 5 cm) and a triangle on top with a base of 12 cm and height 4 cm. Break down the shape to find the total area.
[3 marks]6.
A garden bed is in the shape of an L with two rectangles: one 10 m by 4 m, and another 6 m by 3 m. The overlapping section is 2 m by 2 m. Find the total area of the garden bed by breaking it down.
[4 marks]7.
A shape consists of a rectangle (15 cm by 10 cm) with a smaller rectangle (5 cm by 4 cm) removed from one corner. Show your working to find the remaining area.
[3 marks]8.
A complex figure includes a square (6 cm sides) with a semicircular segment attached. Decompose the shape and calculate the total area, considering the shape as a square plus a semicircle.
[4 marks]9.
A classroom layout includes a rectangular main area (20 m by 15 m) with a smaller rectangular storage extension (5 m by 4 m) attached. Break down the layout into parts to find the total area.
[3 marks]10.
Error Analysis: A student calculates the area of a shape by summing the areas of two rectangles: 8 cm by 3 cm and 4 cm by 2 cm, giving 28 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