Compound Shapes And Parts Of Shapes
Overview
Real objects are rarely a single neat rectangle or circle. An L-shaped room, a running track, a washer with a hole in it: these are compound shapes, built from simpler shapes joined together or cut apart. The good news is that you already know all the formulas you need. The skill is deciding how to split the shape and whether to add or subtract.
In this lesson you will find the area of compound shapes by splitting them into known shapes and adding the parts, and the area of shapes with a piece removed by subtracting. The same add-and-subtract thinking extends to compound solids and their volumes. Master the splitting strategy and even awkward-looking shapes become a short, tidy calculation.
Objectives
- Carry out calculations and solve problems involving perimeters and areas of: compound shapes parts of shapes.
- Carry out calculations and solve problems involving surface areas and volumes of: compound solids parts of solids.
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Lesson Evaluation
Congratulations on completing the lesson on Compound Shapes And Parts Of Shapes. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- An L-shape splits into a rectangle 8 cm by 2 cm and a rectangle 3 cm by 4 cm. What is its total area? A. 17 cm^2 B. 24 cm^2 C. 28 cm^2 D. 48 cm^2 Answer: C
- A circle of radius 3 cm is cut from a square of side 10 cm. Using pi = 3.142, what is the area remaining to 2 d.p.? A. 28.28 cm^2 B. 71.72 cm^2 C. 90.58 cm^2 D. 100.00 cm^2 Answer: B
- A compound solid is a cuboid 5 cm by 4 cm by 3 cm with a cuboid 2 cm by 2 cm by 3 cm on top. What is its volume? A. 60 cm^3 B. 72 cm^3 C. 84 cm^3 D. 120 cm^3 Answer: B
- What is the best first step when finding the area of a compound shape? A. Square the longest side B. Split it into simpler shapes you can calculate C. Multiply all the given lengths together D. Add up every length given Answer: B
- A washer is a circle of radius 5 cm with a circle of radius 2 cm removed from its centre. Using pi = 3.142, what is its area to 2 d.p.? A. 12.57 cm^2 B. 65.98 cm^2 C. 78.55 cm^2 D. 91.12 cm^2 Answer: B
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