This Composite Figure Is Made Up Of Three Simpler Shapes. What Is The Area Of The Figure? A Vertical Quadrilateral Placed Over A Horizontal Parallelogram With Side 12 Cm. The Length Of The Perpendicular Drawn From The Vertex Of The Parallelogram To Its
A composite figure is a geometric shape that is made up of simpler shapes. In this case, we have a vertical quadrilateral placed over a horizontal parallelogram. The area of the composite figure can be found by calculating the area of the individual shapes and then adding them together.
Breaking Down the Figure
To find the area of the composite figure, we need to break it down into its individual components. The vertical quadrilateral has a base of 12 cm and a height of 8 cm. The horizontal parallelogram has a base of 12 cm and a height of 6 cm.
Calculating the Area of the Quadrilateral
The area of a quadrilateral can be found using the formula:
Area = (base × height) / 2
In this case, the base of the quadrilateral is 12 cm and the height is 8 cm. Plugging these values into the formula, we get:
Area = (12 × 8) / 2 = 96 / 2 = 48
Calculating the Area of the Parallelogram
The area of a parallelogram can be found using the formula:
Area = base × height
In this case, the base of the parallelogram is 12 cm and the height is 6 cm. Plugging these values into the formula, we get:
Area = 12 × 6 = 72
Finding the Overlapping Area
The vertical quadrilateral and the horizontal parallelogram overlap, creating a smaller rectangle. The area of this rectangle can be found by multiplying the base and height of the rectangle.
The base of the rectangle is 6 cm (the height of the parallelogram) and the height is 8 cm (the height of the quadrilateral). Plugging these values into the formula, we get:
Area = 6 × 8 = 48
Calculating the Total Area
To find the total area of the composite figure, we need to add the areas of the individual shapes and subtract the overlapping area.
The area of the quadrilateral is 48, the area of the parallelogram is 72, and the overlapping area is 48. Plugging these values into the formula, we get:
Total Area = Area of Quadrilateral + Area of Parallelogram - Overlapping Area = 48 + 72 - 48 = 72
Conclusion
In conclusion, the area of the composite figure is 72 square centimeters. This can be found by breaking down the figure into its individual components, calculating the area of each shape, and then adding them together and subtracting the overlapping area.
Key Takeaways
- A composite figure is a geometric shape made up of simpler shapes.
- The area of a composite figure can be found by calculating the area of the individual shapes and then adding them together.
- The area of a quadrilateral can be found using the formula: Area = (base × height) / 2.
- The area of a parallelogram can be found using the formula: Area = base × height.
- The overlapping area of two shapes can be found by multiplying the base and height of the rectangle formed by the overlap.
Real-World Applications
Understanding the area of composite figures is important in a variety of real-world applications, including:
- Architecture: When designing buildings, architects need to calculate the area of complex shapes to determine the amount of materials needed.
- Engineering: Engineers need to calculate the area of complex shapes to determine the amount of materials needed for construction projects.
- Art: Artists need to calculate the area of complex shapes to determine the amount of materials needed for their projects.
Final Thoughts
Q: What is a composite figure?
A: A composite figure is a geometric shape that is made up of simpler shapes. It can be a combination of two or more basic shapes, such as triangles, quadrilaterals, and polygons.
Q: How do I find the area of a composite figure?
A: To find the area of a composite figure, you need to break it down into its individual components, calculate the area of each shape, and then add them together and subtract the overlapping area.
Q: What is the formula for finding the area of a quadrilateral?
A: The formula for finding the area of a quadrilateral is: Area = (base × height) / 2.
Q: What is the formula for finding the area of a parallelogram?
A: The formula for finding the area of a parallelogram is: Area = base × height.
Q: How do I find the overlapping area of two shapes?
A: To find the overlapping area of two shapes, you need to multiply the base and height of the rectangle formed by the overlap.
Q: What is the difference between a composite figure and a compound shape?
A: A composite figure is a geometric shape that is made up of simpler shapes, while a compound shape is a shape that is made up of two or more basic shapes that are joined together.
Q: Can I use the same formula to find the area of a composite figure and a compound shape?
A: No, you cannot use the same formula to find the area of a composite figure and a compound shape. The formula for finding the area of a composite figure is different from the formula for finding the area of a compound shape.
Q: How do I determine if a shape is a composite figure or a compound shape?
A: To determine if a shape is a composite figure or a compound shape, you need to look at the individual components that make up the shape. If the shape is made up of simpler shapes that are joined together, it is a composite figure. If the shape is made up of two or more basic shapes that are joined together, it is a compound shape.
Q: Can I use the same method to find the area of a composite figure and a compound shape?
A: No, you cannot use the same method to find the area of a composite figure and a compound shape. The method for finding the area of a composite figure is different from the method for finding the area of a compound shape.
Q: What are some real-world applications of composite figures and compound shapes?
A: Composite figures and compound shapes have a variety of real-world applications, including:
- Architecture: When designing buildings, architects need to calculate the area of complex shapes to determine the amount of materials needed.
- Engineering: Engineers need to calculate the area of complex shapes to determine the amount of materials needed for construction projects.
- Art: Artists need to calculate the area of complex shapes to determine the amount of materials needed for their projects.
Q: Can I use technology to help me find the area of a composite figure or a compound shape?
A: Yes, you can use technology to help you find the area of a composite figure or a compound shape. There are many online tools and software programs available that can help you calculate the area of complex shapes.
Q: What are some common mistakes to avoid when finding the area of a composite figure or a compound shape?
A: Some common mistakes to avoid when finding the area of a composite figure or a compound shape include:
- Not breaking down the shape into its individual components
- Not calculating the area of each shape correctly
- Not subtracting the overlapping area
- Not using the correct formula or method
Q: Can I find the area of a composite figure or a compound shape by hand?
A: Yes, you can find the area of a composite figure or a compound shape by hand. However, it may be more difficult and time-consuming than using technology.