Understanding Composite Figures: Perimeter and Area
Composite figures are geometric shapes that are made up of two or more simpler shapes, such as triangles, quadrilaterals, and polygons. In this article, we will explore how to calculate the perimeter and area of composite figures. We will also provide a worksheet for practice.
What are Composite Figures?
Composite figures are shapes that can be divided into two or more simpler shapes. These shapes can be combined in various ways to form more complex figures. Composite figures can be found in real-life objects, such as buildings, bridges, and machines.
Perimeter of Composite Figures
The perimeter of a composite figure is the total distance around the shape. To calculate the perimeter, we need to find the length of each side and add them up. Here are the steps to follow:
- Identify the individual shapes that make up the composite figure.
- Calculate the perimeter of each individual shape.
- Add up the perimeters of all the individual shapes.
📝 Note: Make sure to include the length of any shared sides only once in your calculation.
Area of Composite Figures
The area of a composite figure is the total amount of space inside the shape. To calculate the area, we need to find the area of each individual shape and add them up. Here are the steps to follow:
- Identify the individual shapes that make up the composite figure.
- Calculate the area of each individual shape.
- Add up the areas of all the individual shapes.
📝 Note: Make sure to use the correct formula for the area of each individual shape.
Worksheet Practice
Now that we have learned how to calculate the perimeter and area of composite figures, let’s practice with some examples. Here is a worksheet to help you reinforce your understanding:
| Figure | Perimeter | Area |
|---|---|---|
| A triangle with a base of 5 cm and a height of 6 cm, attached to a rectangle with a length of 8 cm and a width of 4 cm. | ____________ | ____________ |
| A circle with a radius of 3 cm, attached to a square with a side length of 6 cm. | ____________ | ____________ |
| A trapezoid with a base of 8 cm, a height of 5 cm, and a top base of 6 cm, attached to a triangle with a base of 4 cm and a height of 5 cm. | ____________ | ____________ |
Answers
Here are the answers to the worksheet:
| Figure | Perimeter | Area |
|---|---|---|
| A triangle with a base of 5 cm and a height of 6 cm, attached to a rectangle with a length of 8 cm and a width of 4 cm. | 5 + 6 + 8 + 4 = 23 cm | (1/2) × 5 × 6 = 15 cm² + 8 × 4 = 32 cm² = 47 cm² |
| A circle with a radius of 3 cm, attached to a square with a side length of 6 cm. | 2 × π × 3 = 18.84 cm + 4 × 6 = 24 cm = 42.84 cm | π × 3² = 28.27 cm² + 6² = 36 cm² = 64.27 cm² |
| A trapezoid with a base of 8 cm, a height of 5 cm, and a top base of 6 cm, attached to a triangle with a base of 4 cm and a height of 5 cm. | 8 + 5 + 6 + 4 = 23 cm | (1/2) × (8 + 6) × 5 = 35 cm² + (1/2) × 4 × 5 = 10 cm² = 45 cm² |
In conclusion, composite figures are shapes that are made up of two or more simpler shapes. To calculate the perimeter and area of composite figures, we need to identify the individual shapes, calculate the perimeter and area of each shape, and add them up. With practice, you can become proficient in calculating the perimeter and area of composite figures.
What is a composite figure?
+A composite figure is a geometric shape that is made up of two or more simpler shapes, such as triangles, quadrilaterals, and polygons.
How do I calculate the perimeter of a composite figure?
+To calculate the perimeter of a composite figure, identify the individual shapes, calculate the perimeter of each shape, and add them up.
How do I calculate the area of a composite figure?
+To calculate the area of a composite figure, identify the individual shapes, calculate the area of each shape, and add them up.
