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Questions and Answers
What is the first step in finding the area of a compound shape?
What is the formula for the area of a triangle?
What do you do with the areas of each individual shape in a compound shape?
What is the formula for the area of a circle?
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What is the purpose of labeling each shape and its dimensions clearly?
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What should you do to ensure accuracy in your calculations?
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Study Notes
Area of Compound Shapes
A compound shape is a shape that is made up of two or more simpler shapes. To find the area of a compound shape, we need to find the area of each individual shape and then add them together.
Formulae
- Area of a rectangle:
A = l × w - Area of a triangle:
A = ½ × b × h - Area of a circle:
A = π × r^2
Steps to find the area of a compound shape
- Identify the individual shapes: Break down the compound shape into its individual shapes, such as rectangles, triangles, and circles.
- Find the area of each shape: Use the relevant formula to find the area of each individual shape.
- Add the areas together: Add up the areas of each individual shape to find the total area of the compound shape.
Examples
- A rectangle with a triangle on top:
- Find the area of the rectangle:
A = l × w - Find the area of the triangle:
A = ½ × b × h - Add the areas together:
total area = rectangle area + triangle area
- Find the area of the rectangle:
- A circle with a rectangle inside:
- Find the area of the circle:
A = π × r^2 - Find the area of the rectangle:
A = l × w - Subtract the rectangle area from the circle area:
total area = circle area - rectangle area
- Find the area of the circle:
Tips and Tricks
- Make sure to label each shape and its dimensions clearly to avoid confusion.
- Use the correct formula for each shape.
- Double-check your calculations to ensure accuracy.
Area of Compound Shapes
- A compound shape is made up of two or more simpler shapes.
Formulae
- Area of a rectangle:
A = l × w - Area of a triangle:
A = ½ × b × h - Area of a circle:
A = π × r^2
Finding the Area of a Compound Shape
- Break down the compound shape into individual shapes: rectangles, triangles, and circles.
- Find the area of each individual shape using the relevant formula.
- Add the areas of each individual shape together to find the total area.
Examples
- For a rectangle with a triangle on top: calculate the area of the rectangle and triangle separately, then add them together.
- For a circle with a rectangle inside: calculate the area of the circle and rectangle separately, then subtract the rectangle area from the circle area.
Tips and Tricks
- Clearly label each shape and its dimensions to avoid confusion.
- Use the correct formula for each shape.
- Double-check calculations to ensure accuracy.
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Description
Learn how to find the area of compound shapes by breaking them down into individual shapes and applying formulas for rectangles, triangles, and circles.
