To solve the problem, we need to determine the areas of regions
A and
B as shown in the diagram. Let's break it down step by step.
Step 1: Identify the dimensions and shapes
- The entire rectangle has a length of 60 inches and a height of 50 inches.
- Region
A is a rectangle with a length of 60 inches and a height of 25 inches.
- Region
B is a smaller rectangle with a length of 20 inches and a height of 25 inches.
Step 2: Calculate the area of region A
The area of a rectangle is given by the formula:
\[
\text{Area} = \text{length} \times \text{height}
\]
For region
A:
\[
\text{Area of A} = 60 \, \text{in} \times 25 \, \text{in} = 1500 \, \text{square inches}
\]
Step 3: Calculate the area of region B
For region
B:
\[
\text{Area of B} = 20 \, \text{in} \times 25 \, \text{in} = 500 \, \text{square inches}
\]
Step 4: Verify the total area
To ensure our calculations are correct, we can verify the total area of the entire rectangle and compare it with the sum of the areas of regions
A and
B plus the remaining part of the large rectangle.
The total area of the entire rectangle is:
\[
\text{Total area} = 60 \, \text{in} \times 50 \, \text{in} = 3000 \, \text{square inches}
\]
The remaining part of the large rectangle (not included in
A or
B) is a rectangle with a length of 40 inches (since \(60 - 20 = 40\)) and a height of 25 inches. Its area is:
\[
\text{Area of remaining part} = 40 \, \text{in} \times 25 \, \text{in} = 1000 \, \text{square inches}
\]
Now, sum the areas of
A,
B, and the remaining part:
\[
\text{Total area} = \text{Area of A} + \text{Area of B} + \text{Area of remaining part} = 1500 + 500 + 1000 = 3000 \, \text{square inches}
\]
This matches the total area of the large rectangle, confirming our calculations are correct.
Final Answer
The areas of regions
A and
B are:
\[
\boxed{1500 \text{ square inches}, 500 \text{ square inches}}
\]
Parent Tip: Review the logic above to help your child master the concept of area of irregular shapes worksheet.
