To find the area of the composite figure described, we will break it down into manageable parts.
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Identify the shape:
- The description indicates a main rectangle with dimensions for the right side (height) as 4 cm and the bottom side (width) as 10 cm.
- There’s also an extension on the left side that goes upward 7 cm, adding to the height of the figure.
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Calculate the area of the main rectangle:
- The area of the rectangle can be calculated using the formula: \[ \text{Area} = \text{width} \times \text{height} = 10 , \text{cm} \times 4 , \text{cm} = 40 , \text{cm}^2 \]
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Calculate the area of the left extension:
- The extension at the top would be a rectangle with a width equal to the width of the base (10 cm) and a height of 7 cm: \[ \text{Area of the extension} = \text{width} \times \text{height} = 10 , \text{cm} \times 7 , \text{cm} = 70 , \text{cm}^2 \]
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Combine the areas:
- The total area of the composite figure is the sum of the area of the main rectangle and the area of the left extension: \[ \text{Total Area} = \text{Area of the rectangle} + \text{Area of the extension} = 40 , \text{cm}^2 + 70 , \text{cm}^2 = 110 , \text{cm}^2 \]
However, based on the available choices, we must have made a mistake in understanding which areas to combine. Since you mention a few definite response options, it suggests that I may need to reevaluate which specific areas should be considered.
Please provide clarity on whether the left extension is meant to be a part of the main rectangle or if we're supposed to subtract out any overlaps, since the detailed response is not matching standard calculations so far provided.
Final Analysis:
Nonetheless, if we were to just find the relevant total area, none of the options match with finally calculated 110 \(cm^2\). A further check could be all components in case of overlaps (such as redundant sections) also affects final area.
But as it stands, given the straightforward areas involved above, make sure if 110 can be simplified further relevance for divider, or that extension was not treated the way intended. If no, then a review must yield:
- 61 square centimeters - None align directly here given areas described measure.
- 49,21, 40 - all derived simplistic drawer, but numbers lead back again to composite area estimate threshold that doesn't yield listed precision value correspond.
If however there’s assurance rounded out as clarified details alternating solutions render differently outside calculation leads factors left aside, additional clarification would solve analytical gaps.
Thus, finalize attributes together checking on systematic overlays made.
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