Area of Compound Shapes
The area of a compound shape is found by splitting it into simpler shapes like rectangles and triangles. Find each area, such as length × width, then add them for the total area. You subtract instead when a part is cut out.
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Area of a Compound Shape
- A compound shape is made by joining two or more simple shapes.
- To find the area, break it into familiar shapes such as rectangles, triangles, or circles.
- Example: Two Rectangles
- An L-shaped figure can be split into two rectangles.
- Find each rectangle’s area using length × width.
- Add the two areas to get the total area.
Example: Mixed Shapes
- Find the area of each shape separately, such as a rectangle and a triangle.
- The triangle area formula is base × height.
- Add the areas together to get the total area.
Real-Life Application
- Always calculate the total area before finding costs.
- Subtract areas for holes like doors or windows.
- Multiply the area by the price per square metre.
Practice Questions
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A compound shape is made of a square of , and a rectangle of . What is the area of the compound shape?
Correct! 🎉 +10 pointsNot quite right
To find the area of the compound shape, simply add the areas of the square () and the rectangle (). This gives you .
A compound shape is made of a square of , and a triangle of . What is the area of the compound shape?
Correct! 🎉 +10 pointsNot quite right
To find the area of the compound shape, add the areas of the square and the triangle: .
A compound shape consists of a rectangle with an area of and a triangle with a base of and a height of . What is the area of the compound shape?
Correct! 🎉 +20 pointsNot quite right
The area of the triangle is . Adding this to the rectangle’s area () gives a total area of .
A compound shape consists of a rectangle with a length of and a width of , and a triangle with an area of . What is the area of the compound shape?
Correct! 🎉 +20 pointsNot quite right
The rectangle’s area is length × width: . Adding the triangle’s area () gives a total of .
A compound shape consists of a square with side length of and two triangles, each having an area of . What is the area of the compound shape?
Correct! 🎉 +20 pointsNot quite right
The square’s area is side × side: . The two triangles have a total area of . Adding them gives .
A compound shape consists of a rectangle with a length of and a width of , and a semicircle with a radius of . What is the area of the compound shape?
Correct! 🎉 +30 pointsNot quite right
The area of the rectangle is . The area of the semicircle is half the area of a full circle: . Adding them gives .
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Practice: Area of Compound Shape
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Students Also Ask
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A compound shape is a figure made up of two or more simple shapes joined together. Examples include rectangles, triangles, and circles. You see compound shapes often in geometry questions. To find the total area, you usually break the compound shape down into the simple shapes inside.
To find the area of a compound shape, break it down into simpler shapes like rectangles, triangles, and circles. Work out the area of each simple shape using its formula, then add or subtract those areas. Whether you add or subtract depends on how the compound shape is built.
No, there is no single formula. A compound shape combines two or more simpler shapes. For a rectangle, use length × width. For a circle, use π × r². Then add or subtract each individual area to get the total of the compound shape.
You add areas when shapes are joined to form the compound shape. An example is a rectangle joined to a right-angled triangle. You subtract when a smaller shape is cut out of a larger one. An example is a door or a circular window inside a rectangular wall.
Yes. A compound shape can include a circle or part of one. To find its area, use the formula π × r². Here, r is the radius. Add or subtract this area as needed. Add if the circle joins the shape. Subtract if the circle is cut out of it.