Example Question - composite shape
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Calculating Area of Composite Shape
To find the area of the shape in the image, the shape can be broken down into rectangular parts. With the given dimensions, we can configure two rectangles: 1. The first rectangle or the larger part has a length of 15 meters. We need to find the width of this part. By analyzing the dimensions given for the smaller parts, we can see that the overall width must be 8 meters (since one side is 8 meters and the width is consistent across that length). 2. The second rectangle has a length that is the difference between 15 meters and 5 meters (the length of the overlap), which is 10 meters. It has a width of 5 meters. Once we have identified these two rectangles, we can calculate their areas and sum them up: Area of larger rectangle: \(15 m \times 8 m = 120 m^2\) Area of smaller rectangle: \(10 m \times 5 m = 50 m^2\) Adding these two areas together: Total area = \(120 m^2 + 50 m^2 = 170 m^2\) Therefore, the area of the given shape is 170 square meters.
Calculating Area of Composite Shape
The image appears to show a composite shape consisting of a rectangle and a right-angled triangle attached to it. The rectangle has dimensions of 6 cm by 8 cm, and the triangle shares its height of 6 cm with the rectangle and has a base of 4 cm (since the combined base of the rectangle and triangle is 12 cm, and the rectangle alone is 8 cm). To calculate the area of this shape, we need to find the area of both the rectangle and the triangle and then add these together. Area of the rectangle: \( A_{rectangle} = \text{length} \times \text{width} \) \( A_{rectangle} = 8\, \text{cm} \times 6\, \text{cm} \) \( A_{rectangle} = 48\, \text{cm}^2 \) Area of the triangle: The area of a right-angled triangle can be found using the formula: \( A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} \) \( A_{triangle} = \frac{1}{2} \times 4\, \text{cm} \times 6\, \text{cm} \) \( A_{triangle} = \frac{1}{2} \times 24\, \text{cm}^2 \) \( A_{triangle} = 12\, \text{cm}^2 \) Now, we add the area of the rectangle and the area of the triangle to get the total area. Total area: \( A_{total} = A_{rectangle} + A_{triangle} \) \( A_{total} = 48\, \text{cm}^2 + 12\, \text{cm}^2 \) \( A_{total} = 60\, \text{cm}^2 \) So, the combined area of the composite shape is 60 square centimeters.
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