To find the area of the poster as described, let's analyze the points and the shape they form.
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Identifying the Quadrilateral (Bottom Portion): The bottom portion of the figure is the quadrilateral formed by points A (4, 2), D (8, 2), and E (2, 2). The points B (4, 12) and C (8, 12) are part of the upper section.
We can visualize the base of this quadrilateral:
- The bottom side extends from E (2, 2) to G (10, 2).
- The quadrilateral is a trapezoid with points A, D, F at the bottom and F at the top.
The base of this rectangle formed by points A, D is \[ \text{Base} = 8 - 2 = 6 , \text{meters.} \]
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Area of the Composed Rectangle: The height of the rectangle formed can be determined from point B and point A: \[ \text{Height} = 12 - 2 = 10 , \text{meters.} \]
The area of this composed rectangle is \[ \text{Area} = \text{Base} \times \text{Height} = 6 \times 10 = 60 , \text{square meters.} \]
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Triangles to be Subtracted: To find the total area of the figure, we need to subtract two triangles:
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For triangle ADF, the base = \(AD\) = 8 - 4 = 4 meters
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The height = \(F\)'s y-coordinates = 18 - 2 = 16 meters
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Area of triangle ADF is: \[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 4 \times 16 = 32 , \text{square meters.} \]
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Total Area Calculation: Therefore, the total area of the poster is: \[ \text{Total Area} = \text{Area of Rectangle} - \text{Area of Triangle ADF} = 60 - 32 = 28 , \text{square meters.} \]
Putting this together into the requested format:
- Base of the rectangle: 6
- Area of the composed rectangle: 60
- Base of each triangle: 4
- Height of each triangle: 16
- Area of triangle ADF: 32
- Total area of the poster: 28
Now you can select these options in the drop-down menus as required!
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