Breaking Down: Problem Solving & Reasoning
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on breaking down complex shapes into simpler parts to find the total area. It develops understanding of additive methods for compound shapes through problem solving and reasoning tasks.
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Breaking Down: Problem Solving & Reasoning
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 a rectangle measuring 8 cm by 3 cm.
[2 marks]2.
A L-shaped figure is formed by a 10 cm by 4 cm rectangle and a 6 cm by 3 cm rectangle joined together. Break down the shape and find its total area.
[4 marks]3.
Decompose a complex shape into two rectangles, one 12 cm by 5 cm and the other 7 cm by 4 cm. How much is the combined area?
[3 marks]4.
Construct a shape made of two rectangles: one 9 cm by 4 cm and the other 5 cm by 3 cm, sharing a side. Calculate the total area.
[3 marks]5.
A shape consists of a square (6 cm sides) attached to a rectangle (8 cm by 4 cm). Break it down and find the total area.
[3 marks]6.
A composite shape includes a triangle of base 6 cm and height 4 cm, and a rectangle measuring 5 cm by 3 cm. Find the total area.
[4 marks]7.
A large rectangle is divided into two smaller rectangles, one 15 cm by 8 cm and the other 10 cm by 6 cm. Calculate the sum of their areas.
[3 marks]8.
A shape is made by combining a rectangle (10 cm by 4 cm) and a square (4 cm sides). Break down the shape and find total area.
[3 marks]9.
A complex shape can be divided into three rectangles: 8 cm by 3 cm, 6 cm by 4 cm, and 5 cm by 2 cm. Find the total area.
[4 marks]10.
A shape involves a rectangle with dimensions 12 cm by 7 cm and a triangle of base 8 cm and height 3 cm, sharing a side. Break it down and compute total area.
[4 marks]11.
Identify the mistake: A student decomposes a 20 cm by 10 cm rectangle into two parts: 12 cm by 10 cm and 8 cm by 10 cm, then adds areas. The student claims total area as 300 cm². Is this correct? If not, correct the mistake.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet