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What is the area of the composite figure?
Bottom base: 7 mi
Side base length: 6 mi
Left tower side: 3 mi
Left tower top: 1 mi
Right tower side: 1 mi
right tower top 1 mi
Bottom base: 7 mi
Side base length: 6 mi
Left tower side: 3 mi
Left tower top: 1 mi
Right tower side: 1 mi
right tower top 1 mi
Answers
Answered by
GPT-4o mini
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
1. **Bottom Rectangle (Base)**:
- Length: 7 mi (the bottom base)
- Width: 6 mi (the side base)
2. **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.
3. **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
1. **Area of the Rectangle (Base)**:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 7 \, \text{mi} \times 6 \, \text{mi} = 42 \, \text{mi}^2
\]
2. **Area of Left Tower**:
- The height is 3 mi and the top width is 1 mi.
- 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.
- \[
\text{Area}_{\text{left rectangle}} = \text{height} \times \text{top width} = 3 \, \text{mi} \times 1 \, \text{mi} = 3 \, \text{mi}^2
\]
3. **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 \( \text{46 mi}^2 \).
### Step 1: Identify the components
1. **Bottom Rectangle (Base)**:
- Length: 7 mi (the bottom base)
- Width: 6 mi (the side base)
2. **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.
3. **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
1. **Area of the Rectangle (Base)**:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 7 \, \text{mi} \times 6 \, \text{mi} = 42 \, \text{mi}^2
\]
2. **Area of Left Tower**:
- The height is 3 mi and the top width is 1 mi.
- 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.
- \[
\text{Area}_{\text{left rectangle}} = \text{height} \times \text{top width} = 3 \, \text{mi} \times 1 \, \text{mi} = 3 \, \text{mi}^2
\]
3. **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 \( \text{46 mi}^2 \).