Calculate the area of the given shape in cm².
Understand the Problem
The question asks for the area of a composite shape that includes rectangles and possibly a triangle, given specific dimensions. To find the area, we will likely need to calculate the area of the rectangles separately and then potentially sum or subtract areas based on the shape given.
Answer
The total area of the composite shape is $1028 \, \text{cm}^2$.
Answer for screen readers
The total area of the composite shape is $1028 , \text{cm}^2$.
Steps to Solve
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Identify the Shapes in the Composite Area The composite shape involves rectangles and potentially a smaller rectangle or triangle that needs to be accounted for. We will separate the larger shape into recognizable components.
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Calculate the Area of the Outer Rectangle The outer rectangle dimensions are 56 cm by 23 cm. [ \text{Area}_{\text{outer}} = 56 , \text{cm} \times 23 , \text{cm} = 1288 , \text{cm}^2 ]
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Calculate the Area of the Cut-out Rectangle The dimensions of the rectangle that is cut out (from the right side) are 20 cm by (28 cm - 15 cm = 13 cm). [ \text{Area}_{\text{cut-out}} = 20 , \text{cm} \times 13 , \text{cm} = 260 , \text{cm}^2 ]
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Calculate the Total Area of the Composite Shape Subtract the area of the cut-out rectangle from the area of the outer rectangle. [ \text{Area}{\text{total}} = \text{Area}{\text{outer}} - \text{Area}_{\text{cut-out}} = 1288 , \text{cm}^2 - 260 , \text{cm}^2 = 1028 , \text{cm}^2 ]
The total area of the composite shape is $1028 , \text{cm}^2$.
More Information
The area of a composite shape can be calculated by finding the area of the individual components and then combining them through addition or subtraction, depending on whether areas are added or removed.
Tips
- Forgetting to subtract the area of cut-out shapes.
- Misreading dimensions from the diagram.
- Not ensuring units are consistent when calculating areas.
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