Question
Plot and Find Area of Polygon (Rectilinear Lengths)
Score: 0/3
Penalty: none
Question
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A, left parenthesis, minus, 6, comma, 9, right parenthesisA(−6,9), B, left parenthesis, minus, 3, comma, 9, right parenthesisB(−3,9), C, left parenthesis, minus, 3, comma, 5, right parenthesisC(−3,5), D, left parenthesis, 6, comma, 9, right parenthesisD(6,9), E, left parenthesis, 6, comma, minus, 2, right parenthesisE(6,−2), F, of, minus, 6, comma, minus, 2F(−6,−2)
Area =
unitssquared
2
Score: 0/3
Penalty: none
Question
Show Examples
Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A, left parenthesis, minus, 6, comma, 9, right parenthesisA(−6,9), B, left parenthesis, minus, 3, comma, 9, right parenthesisB(−3,9), C, left parenthesis, minus, 3, comma, 5, right parenthesisC(−3,5), D, left parenthesis, 6, comma, 9, right parenthesisD(6,9), E, left parenthesis, 6, comma, minus, 2, right parenthesisE(6,−2), F, of, minus, 6, comma, minus, 2F(−6,−2)
Area =
unitssquared
2
Answers
GPT-4o mini
To find the area of the polygon defined by the points A, B, C, D, E, and F, we first need to plot the points and connect them in the given order:
1. **Points to plot:**
- A (-6, 9)
- B (-3, 9)
- C (-3, 5)
- D (6, 9)
- E (6, -2)
- F (-6, -2)
2. **Plotting the points:**
- A to B is a horizontal line segment at \(y = 9\) from \(x = -6\) to \(x = -3\).
- B to C is a vertical line segment from \(y = 9\) to \(y = 5\) (at \(x = -3\)).
- C to D is a horizontal line segment at \(y = 5\) from \(x = -3\) to \(x = 6\).
- D to E is a vertical line segment from \(y = 5\) to \(y = -2\) (at \(x = 6\)).
- E to F is a horizontal line segment at \(y = -2\) from \(x = 6\) to \(x = -6\).
- F to A is a vertical line segment from \(y = -2\) to \(y = 9\) (at \(x = -6\)).
3. **Connecting the points, we visualize the shape as follows:**
- The points create a 5-sided polygon that opens up and down.
### Area Calculation
We can calculate the area by breaking the complex shape into simpler rectangles.
#### Vertically split sections:
1. **Left rectangle between A and F:**
- Width (along \(x\)): \(6 - (-6) = 12\)
- Height (along \(y\)): \(9 - (-2) = 11\)
Area of the left rectangle = \(12 \times 11 = 132\).
2. **Top rectangle above the horizontal segment from B to C:**
- It covers distances between the lines drawn from points:
- Top edges (at y=9 to y=5)
- Bottom edge (at y=5)
Area of the rectangle with base on the x-axis from A to D:
- Width = \(6 - (-6) = 12\)
- Height = \(9 - 5 = 4\)
Area of the top rectangle = \(12 \times 4 = 48\).
3. **Put together the areas:**
- Total Area = Area of left rectangle (132) - Area of top rectangle (48)
\(\text{Total Area} = 132 - 48 = 84\) square units.
Thus, the area of the polygon is:
**Area = 84 square units.**
1. **Points to plot:**
- A (-6, 9)
- B (-3, 9)
- C (-3, 5)
- D (6, 9)
- E (6, -2)
- F (-6, -2)
2. **Plotting the points:**
- A to B is a horizontal line segment at \(y = 9\) from \(x = -6\) to \(x = -3\).
- B to C is a vertical line segment from \(y = 9\) to \(y = 5\) (at \(x = -3\)).
- C to D is a horizontal line segment at \(y = 5\) from \(x = -3\) to \(x = 6\).
- D to E is a vertical line segment from \(y = 5\) to \(y = -2\) (at \(x = 6\)).
- E to F is a horizontal line segment at \(y = -2\) from \(x = 6\) to \(x = -6\).
- F to A is a vertical line segment from \(y = -2\) to \(y = 9\) (at \(x = -6\)).
3. **Connecting the points, we visualize the shape as follows:**
- The points create a 5-sided polygon that opens up and down.
### Area Calculation
We can calculate the area by breaking the complex shape into simpler rectangles.
#### Vertically split sections:
1. **Left rectangle between A and F:**
- Width (along \(x\)): \(6 - (-6) = 12\)
- Height (along \(y\)): \(9 - (-2) = 11\)
Area of the left rectangle = \(12 \times 11 = 132\).
2. **Top rectangle above the horizontal segment from B to C:**
- It covers distances between the lines drawn from points:
- Top edges (at y=9 to y=5)
- Bottom edge (at y=5)
Area of the rectangle with base on the x-axis from A to D:
- Width = \(6 - (-6) = 12\)
- Height = \(9 - 5 = 4\)
Area of the top rectangle = \(12 \times 4 = 48\).
3. **Put together the areas:**
- Total Area = Area of left rectangle (132) - Area of top rectangle (48)
\(\text{Total Area} = 132 - 48 = 84\) square units.
Thus, the area of the polygon is:
**Area = 84 square units.**