Problem:
The task is to find the area of a composite shape, which consists of two rectangles: rectangle \( Y \) and square \( X \). The solution provided uses a specific method to calculate the total area. Let's analyze and explain the solution step by step.
---
Step 1: Understand the Shape
The composite shape is made up of:
1.
Rectangle \( Y \): This is the larger rectangular region.
2.
Square \( X \): This is the smaller square region that overlaps with part of rectangle \( Y \).
From the image:
- Rectangle \( Y \) has dimensions \( 6 \, \text{cm} \times 2 \, \text{cm} \).
- Square \( X \) has a side length of \( 3 \, \text{cm} \).
---
Step 2: Method Used
The solution uses the following approach:
\[
\text{Area of shape} = \text{Area of rectangle } Y + \text{Area of square } X
\]
####
Step 2.1: Calculate the Area of Rectangle \( Y \)
The formula for the area of a rectangle is:
\[
\text{Area} = \text{length} \times \text{width}
\]
For rectangle \( Y \):
\[
\text{Length} = 6 \, \text{cm}, \quad \text{Width} = 2 \, \text{cm}
\]
\[
\text{Area of rectangle } Y = 6 \times 2 = 12 \, \text{cm}^2
\]
####
Step 2.2: Calculate the Area of Square \( X \)
The formula for the area of a square is:
\[
\text{Area} = \text{side}^2
\]
For square \( X \):
\[
\text{Side} = 3 \, \text{cm}
\]
\[
\text{Area of square } X = 3^2 = 9 \, \text{cm}^2
\]
####
Step 2.3: Add the Areas
Since the square \( X \) is entirely within the composite shape and does not overlap with any part outside the shape, we simply add the areas of rectangle \( Y \) and square \( X \):
\[
\text{Total area} = \text{Area of rectangle } Y + \text{Area of square } X
\]
\[
\text{Total area} = 12 + 9 = 21 \, \text{cm}^2
\]
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Step 3: Verify the Solution
- The dimensions of rectangle \( Y \) are correct based on the image.
- The side length of square \( X \) is also correct.
- There is no overlap or subtraction needed since square \( X \) is entirely contained within the composite shape.
Thus, the total area calculation is valid.
---
Final Answer
\[
\boxed{21 \, \text{cm}^2}
\]
Parent Tip: Review the logic above to help your child master the concept of area of composite figures worksheet 7th grade answers.
