To find the area of the composite figure described, we need to break down the shape into simpler components. The figure seems to include a rectangular base and two triangular towers on top of it. Let's break it down step by step:
Step 1: Identify the components
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Bottom Rectangle (Base):
- Length: 7 mi (the bottom base)
- Width: 6 mi (the side base)
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Left Tower:
- Height: 3 mi (left tower side)
- Top Width: 1 mi (left tower top)
- The shape of the left tower can be considered a rectangle on the top with a triangular section on the left.
-
Right Tower:
- Height: 1 mi (right tower side)
- Top Width: 1 mi (right tower top)
- The right tower is similar to the left tower.
Step 2: Calculate areas individually
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Area of the Rectangle (Base): \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 7 , \text{mi} \times 6 , \text{mi} = 42 , \text{mi}^2 \]
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Area of Left Tower:
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The height is 3 mi and the top width is 1 mi.
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The left tower can be viewed as a rectangle (height) on the left and a triangle on the top.
-
Rectangle Area:
- Assume the width of the rectangle tower at the bottom is the same as the bottom base.
- \[ \text{Area}_{\text{left rectangle}} = \text{height} \times \text{top width} = 3 , \text{mi} \times 1 , \text{mi} = 3 , \text{mi}^2 \]
-
-
Area of Right Tower:
- For the right tower, which is similar: \[ \text{Area}_{\text{right rectangle}} = 1 , \text{mi} \times 1 , \text{mi} = 1 , \text{mi}^2 \]
Step 3: Total Area Calculation
To find the total area of the composite figure: \[ \text{Total Area} = \text{Area}{\text{rectangle}} + \text{Area}{\text{left tower}} + \text{Area}_{\text{right tower}} \] Substituting the values calculated: \[ \text{Total Area} = 42 , \text{mi}^2 + 3 , \text{mi}^2 + 1 , \text{mi}^2 = 46 , \text{mi}^2 \]
So, the area of the composite figure is \( \text{46 mi}^2 \).