Understanding the Concept of Combined Rectangles
When dealing with combined rectangles, it’s essential to understand how to calculate the total area of the shape. Combined rectangles are formed when two or more rectangles are joined together to form a new shape. In this worksheet, we’ll explore how to find the area of combined rectangles using simple formulas and examples.
What is the Formula for the Area of Combined Rectangles?
To find the area of combined rectangles, you need to calculate the area of each individual rectangle and then add them together. The formula for the area of a rectangle is:
Area = Length × Width
When dealing with combined rectangles, you’ll need to calculate the area of each rectangle separately and then add them together.
Example 1: Finding the Area of Two Combined Rectangles
Let’s consider an example where we have two rectangles combined together.
Rectangle 1: Length = 6 cm, Width = 4 cm Rectangle 2: Length = 8 cm, Width = 3 cm
To find the total area of the combined rectangles, we’ll calculate the area of each rectangle separately and then add them together.
Area of Rectangle 1 = Length × Width = 6 cm × 4 cm = 24 cm² Area of Rectangle 2 = Length × Width = 8 cm × 3 cm = 24 cm²
Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 24 cm² + 24 cm² = 48 cm²
Example 2: Finding the Area of Three Combined Rectangles
Now, let’s consider an example where we have three rectangles combined together.
Rectangle 1: Length = 5 cm, Width = 2 cm Rectangle 2: Length = 7 cm, Width = 4 cm Rectangle 3: Length = 9 cm, Width = 1 cm
To find the total area of the combined rectangles, we’ll calculate the area of each rectangle separately and then add them together.
Area of Rectangle 1 = Length × Width = 5 cm × 2 cm = 10 cm² Area of Rectangle 2 = Length × Width = 7 cm × 4 cm = 28 cm² Area of Rectangle 3 = Length × Width = 9 cm × 1 cm = 9 cm²
Total Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3 = 10 cm² + 28 cm² + 9 cm² = 47 cm²
Calculating the Area of Combined Rectangles with Different Orientations
When dealing with combined rectangles, it’s essential to consider the orientation of the rectangles. If the rectangles are oriented differently, you may need to adjust your calculations accordingly.
Let’s consider an example where we have two rectangles combined together, but they are oriented differently.
Rectangle 1: Length = 6 cm, Width = 4 cm Rectangle 2: Length = 8 cm, Width = 3 cm (oriented perpendicularly to Rectangle 1)
To find the total area of the combined rectangles, we’ll calculate the area of each rectangle separately and then add them together.
Area of Rectangle 1 = Length × Width = 6 cm × 4 cm = 24 cm² Area of Rectangle 2 = Length × Width = 8 cm × 3 cm = 24 cm²
Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 24 cm² + 24 cm² = 48 cm²
As you can see, the orientation of the rectangles doesn’t affect the total area of the combined shape.
Tables for Combined Rectangles
Here’s a table summarizing the formulas and examples we’ve discussed so far:
| Example | Rectangle 1 | Rectangle 2 | Total Area |
|---|---|---|---|
| Example 1 | Length = 6 cm, Width = 4 cm | Length = 8 cm, Width = 3 cm | 48 cm² |
| Example 2 | Length = 5 cm, Width = 2 cm | Length = 7 cm, Width = 4 cm | 47 cm² |
| Example 3 | Length = 6 cm, Width = 4 cm | Length = 8 cm, Width = 3 cm (oriented perpendicularly) | 48 cm² |
📝 Note: When calculating the area of combined rectangles, make sure to calculate the area of each rectangle separately and then add them together.
Let’s summarize the key points we’ve discussed so far:
- To find the area of combined rectangles, calculate the area of each individual rectangle and then add them together.
- The formula for the area of a rectangle is Area = Length × Width.
- When dealing with combined rectangles, consider the orientation of the rectangles, but it won’t affect the total area of the combined shape.
What is the formula for the area of a rectangle?
+The formula for the area of a rectangle is Area = Length × Width.
How do I calculate the area of combined rectangles?
+To calculate the area of combined rectangles, calculate the area of each individual rectangle and then add them together.
Does the orientation of the rectangles affect the total area of the combined shape?
+No, the orientation of the rectangles doesn't affect the total area of the combined shape.
In conclusion, finding the area of combined rectangles is a straightforward process that involves calculating the area of each individual rectangle and then adding them together. By understanding the formula for the area of a rectangle and considering the orientation of the rectangles, you can easily find the total area of combined rectangles.
Related Terms:
- Compound shape area worksheet
- Area of rectilinear shapes
- Area of a rectangle Worksheet
