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What is the area of a quadrilateral with vertices at (-2,-6), (1,-6), (-2,0), and (1,0)? Enter the answer in the box. units squared

What is the area of a quadrilateral with vertices at (-2,-6), (1,-6), (-2,0), and (1,0)? Enter the answer in the box. units squared

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Calculating the Area of a Quadrilateral** The problem presents a quadrilateral with the vertices at the coordinates \((-2, -6)\), \((1, -6)\), \((-2, 0)\), and \((1, 0)\). To find the area of this quadrilateral, we can use specific methods suitable for coordinate geometry. ### Coordinates of the Quadrilateral: - Vertex 1: \((-2, -6)\) - Vertex 2: \((1, -6)\) - Vertex 3: \((-2, 0)\) - Vertex 4: \((1, 0)\) **Question:** What is the area of the quadrilateral with these given vertices? Enter the answer in the box provided. **Answer Box:** ``` [ ] units squared ``` To find the solution, you can use the Shoelace Theorem (or Gauss's area formula for polygons), which is effective for finding the area using the vertices' coordinates directly. By applying the Shoelace Theorem: \[ Area = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right| \] Substitute the vertices \((-2, -6)\), \((1, -6)\), \((-2, 0)\), and \((1, 0)\) into the formula and perform the calculations to obtain the area. Remember to enter your answer in the provided answer box measured in square units.
Transcribed Image Text:**Calculating the Area of a Quadrilateral** The problem presents a quadrilateral with the vertices at the coordinates \((-2, -6)\), \((1, -6)\), \((-2, 0)\), and \((1, 0)\). To find the area of this quadrilateral, we can use specific methods suitable for coordinate geometry. ### Coordinates of the Quadrilateral: - Vertex 1: \((-2, -6)\) - Vertex 2: \((1, -6)\) - Vertex 3: \((-2, 0)\) - Vertex 4: \((1, 0)\) **Question:** What is the area of the quadrilateral with these given vertices? Enter the answer in the box provided. **Answer Box:** ``` [ ] units squared ``` To find the solution, you can use the Shoelace Theorem (or Gauss's area formula for polygons), which is effective for finding the area using the vertices' coordinates directly. By applying the Shoelace Theorem: \[ Area = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right| \] Substitute the vertices \((-2, -6)\), \((1, -6)\), \((-2, 0)\), and \((1, 0)\) into the formula and perform the calculations to obtain the area. Remember to enter your answer in the provided answer box measured in square units.
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