A 'C' shape has two horizontal rectangles attached to a vertical rectangle. The horizontal rectangles each measure 2 inches by 1 inch and the vertical rectangle measures 4 inches b... A 'C' shape has two horizontal rectangles attached to a vertical rectangle. The horizontal rectangles each measure 2 inches by 1 inch and the vertical rectangle measures 4 inches by 1 inch. What is the area of the figure?
Understand the Problem
The question asks to calculate the area of a 'C' shape comprised of three rectangles. We need to calculate the area of each rectangle and then sum them up to find the total area of the composite shape.
Answer
The total area is $52 \text{ cm}^2$.
Answer for screen readers
The total area of the 'C' shape is $52 \text{ cm}^2$.
Steps to Solve
- Identify the dimensions of the first rectangle
The first rectangle has a height of 10 cm and a width of 2 cm.
- Calculate the area of the first rectangle
The area of a rectangle is given by the formula: $Area = height \times width$. So, the area of the first rectangle is: $10 \times 2 = 20 \text{ cm}^2$.
- Identify the dimensions of the second rectangle
The second rectangle has a height of 2 cm and a width of 6 cm.
- Calculate the area of the second rectangle
Using the formula for the area of a rectangle, the area of the second rectangle is: $2 \times 6 = 12 \text{ cm}^2$.
- Identify the dimensions of the third rectangle
The third rectangle has a height of 10 cm and a width of 2 cm.
- Calculate the area of the third rectangle
The area of the third rectangle is: $10 \times 2 = 20 \text{ cm}^2$.
- Calculate the total area
To find the total area of the 'C' shape, sum the areas of the three rectangles: $20 + 12 + 20 = 52 \text{ cm}^2$.
The total area of the 'C' shape is $52 \text{ cm}^2$.
More Information
The 'C' shape is a composite shape made up of three rectangles. By dividing a complex shape into simpler components, it becomes easier to determine its area or other properties.
Tips
A common mistake is to misidentify the dimensions of the rectangles, especially when they are part of a larger composite shape. Carefully examine the diagram and make sure you are using the correct height and width for each rectangle. Another common mistake could be adding the areas incorrectly.
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