Find the area of the polygon.
Understand the Problem
The question is asking for the area of a polygon with given dimensions. To find the area, we will break down the polygon into recognizable shapes (rectangles, squares, etc.), calculate their areas, and then sum them up to get the total area of the polygon.
Answer
The area of the polygon is \(15 \, \text{cm}^2\).
Answer for screen readers
The area of the polygon is (15 , \text{cm}^2).
Steps to Solve
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Identify the Shapes
We can break down the polygon into two rectangles. The top rectangle has dimensions 3 cm (length) and 1 cm (height) and the bottom part consists of a larger rectangle with dimensions 3 cm (length) and 4 cm (height). -
Calculate the Area of the Top Rectangle
The area (A_1) of the top rectangle can be calculated using the formula for the area of a rectangle:
$$ A_1 = \text{length} \times \text{height} = 3 , \text{cm} \times 1 , \text{cm} = 3 , \text{cm}^2 $$ -
Calculate the Area of the Bottom Rectangle
The area (A_2) of the bottom rectangle can be calculated similarly:
$$ A_2 = \text{length} \times \text{height} = 3 , \text{cm} \times 4 , \text{cm} = 12 , \text{cm}^2 $$ -
Combine the Areas
To find the total area (A) of the polygon, sum the areas of the two rectangles:
$$ A = A_1 + A_2 = 3 , \text{cm}^2 + 12 , \text{cm}^2 = 15 , \text{cm}^2 $$
The area of the polygon is (15 , \text{cm}^2).
More Information
The area calculated includes all segments of the polygon. Understanding how to break complex shapes into simpler rectangles can simplify area calculations significantly.
Tips
- Forgetting to break the polygon into simpler shapes can lead to errors in calculation.
- Miscalculating the dimensions of the rectangles.
- Overlooking units of measurement, which can lead to incorrect answers if not consistently applied.
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