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Questions and Answers
A garden is designed with a rectangular section and a semi-circular section attached to one of its longer sides. The rectangle measures 8 meters by 5 meters, with the semi-circle attached to the 8-meter side. What is the total area of the garden?
A garden is designed with a rectangular section and a semi-circular section attached to one of its longer sides. The rectangle measures 8 meters by 5 meters, with the semi-circle attached to the 8-meter side. What is the total area of the garden?
- 55.7 m²
- 65.7 m² (correct)
- 40 m²
- 62.8 m²
An architect is designing a window that consists of a square with a right-angled triangle on top. The square has sides of 1 meter, and the triangle has a base of 1 meter and a height of 0.5 meters. What is the total area of the window?
An architect is designing a window that consists of a square with a right-angled triangle on top. The square has sides of 1 meter, and the triangle has a base of 1 meter and a height of 0.5 meters. What is the total area of the window?
- 1.5 m²
- 2 m²
- 0.75 m²
- 1.25 m² (correct)
A farmer has a field that is shaped like a rectangle with a smaller rectangular section removed for a barn. The larger rectangle measures 50 meters by 40 meters, and the barn section measures 10 meters by 8 meters. What is the usable area of the field?
A farmer has a field that is shaped like a rectangle with a smaller rectangular section removed for a barn. The larger rectangle measures 50 meters by 40 meters, and the barn section measures 10 meters by 8 meters. What is the usable area of the field?
- 2000 m²
- 1920 m² (correct)
- 2400 m²
- 480 m²
An interior designer is planning to install carpet in a room that is shaped like a rectangle with a quarter-circle section removed from one corner. The rectangle measures 6 meters by 4 meters, and the radius of the quarter-circle is 2 meters. What is the area of the room that needs to be carpeted?
An interior designer is planning to install carpet in a room that is shaped like a rectangle with a quarter-circle section removed from one corner. The rectangle measures 6 meters by 4 meters, and the radius of the quarter-circle is 2 meters. What is the area of the room that needs to be carpeted?
A logo is designed with an equilateral triangle placed on top of a rectangle. The rectangle has a width of 4 cm and a height of 3 cm. The triangle has a base of 4 cm and a height of 3.5 cm. What is the total area of the logo?
A logo is designed with an equilateral triangle placed on top of a rectangle. The rectangle has a width of 4 cm and a height of 3 cm. The triangle has a base of 4 cm and a height of 3.5 cm. What is the total area of the logo?
A running track consists of a rectangle with a semicircle at each end. The rectangle measures 80 meters in length and 20 meters in width. What is the total area enclosed by the track?
A running track consists of a rectangle with a semicircle at each end. The rectangle measures 80 meters in length and 20 meters in width. What is the total area enclosed by the track?
A playground is shaped like a square with a quarter-circle attached to one side. The square has sides of 10 meters, and the quarter-circle has a radius of 10 meters. What is the total area of the playground?
A playground is shaped like a square with a quarter-circle attached to one side. The square has sides of 10 meters, and the quarter-circle has a radius of 10 meters. What is the total area of the playground?
A wall is made of a rectangular section and a triangle on top. The rectangular section is 8 feet high and wide. The triangle has a base of 8 feet and a height of 4 feet. If one can of paint covers 50 square feet, how many cans of paint are needed to paint the wall?
A wall is made of a rectangular section and a triangle on top. The rectangular section is 8 feet high and wide. The triangle has a base of 8 feet and a height of 4 feet. If one can of paint covers 50 square feet, how many cans of paint are needed to paint the wall?
Consider a composite shape formed by a square with side length 's' and a smaller square of side length 's/2' cut out from its center. A circle with radius 's/4' is inscribed within the smaller square. Determine the area of shaded region after cutting out the smaller square and circle.
Consider a composite shape formed by a square with side length 's' and a smaller square of side length 's/2' cut out from its center. A circle with radius 's/4' is inscribed within the smaller square. Determine the area of shaded region after cutting out the smaller square and circle.
An emblem consists of a regular hexagon circumscribed about a circle. If the radius of the circle is 'r', what is the area of the region inside the hexagon but outside the circle?
An emblem consists of a regular hexagon circumscribed about a circle. If the radius of the circle is 'r', what is the area of the region inside the hexagon but outside the circle?
Flashcards
What are composite figures?
What are composite figures?
Shapes made up of two or more basic geometric shapes.
Area of a Triangle
Area of a Triangle
Area = 1/2 * base * height
Area of a Circle
Area of a Circle
Area = π * radius² (π ≈ 3.14159)
Area of a Semicircle
Area of a Semicircle
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Area of a Square
Area of a Square
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Area of a Rectangle
Area of a Rectangle
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Area of Composite Figures
Area of Composite Figures
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Architecture Application
Architecture Application
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Landscaping Application
Landscaping Application
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Interior Design Application
Interior Design Application
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Study Notes
- Composite figures consist of two or more basic geometric shapes.
- To find the area of composite figures, calculate the area of each shape then combine (add or subtract) as necessary.
Basic Area Formulas
- Triangle area equals 1/2 * base * height.
- Circle area equals π * radius², where π ≈ 3.14159.
- Semicircle area equals 1/2 * π * radius².
- Square area equals side².
- Rectangle area equals length * width.
Area Calculations for Composite Figures
- Identify the basic shapes forming the composite figure.
- Calculate each shape's area using the correct formula.
- Add areas if shapes are combined, subtract if one is removed.
- Use the same units for all measurements before calculating.
- Divide complex shapes into smaller parts for easier calculation.
Examples of Area Calculations
- For a rectangle and triangle composite:
- Find the rectangle's area (length * width).
- Find the triangle's area (1/2 * base * height).
- Add these areas for the total area.
- For a square with a semicircle on top:
- Calculate the square's area (side²).
- Calculate the semicircle's area (1/2 * π * radius²), with the radius being half the square's side.
- Add the two areas.
- For a rectangle with a circle cut out:
- Determine the area of the rectangle (length * width).
- Determine the area of the circle (π * radius²).
- Subtract the circle's area from the rectangle's area.
Real-Life Applications
- Architecture and Construction:
- To work out area of irregular rooms or buildings.
- To find material needs for flooring, roofing, or walls.
- Landscaping:
- To estimate grass, mulch, or paving stone needs.
- To plan layouts for flower beds and pathways.
- Interior Design:
- To find wall area for painting or wallpapering.
- To plan furniture size and placements.
- Engineering:
- To design complex machine parts/structures.
- To calculate surface area for thermal/fluid analysis.
- City Planning:
- For sizing parks with different geometric shapes.
- For estimating land usage and zoning.
- Manufacturing:
- Needed to calculate material for composite shapes.
- Used to optimize part layouts for less waste.
- Fashion Design:
- Creating patterns by combining different shapes/sizes.
- Estimating fabric needed for garments.
- Agriculture:
- For crop yield estimations in irregular fields.
- For optimizing irrigation/fertilization.
- Real Estate:
- To work out property values based on land/structure area.
- To help divide land into plots for sale.
- Mapping and Surveying:
- Calculating land area using aerial/satellite imagery.
- For creating maps for navigation.
- Sports:
- Used to determine the sizes of sports fields with various geometric shapes.
- Designing equipment or facilities that meet specific size and shape requirements.
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