trapezoid
b1 ... (-2,2)-->(3,2)
b2 ... (-2,-5)-->(7,-5)
h ... (-2,-5)-->(-2,2)
What is the area of a polygon with vertices of (–2, 2), (3, 2), (7, –5), and (–2, –5)?
3 answers
To find the area of a polygon with given vertices, we can use the Shoelace Formula.
The Shoelace Formula calculates the area of a polygon by taking the sum of the products of the coordinates of consecutive vertices, with one additional product of the last vertex with the first vertex, and subtracting the sum of the products of the coordinates of consecutive vertices in reverse order.
Given the vertices: A(-2, 2), B(3, 2), C(7, -5), and D(-2, -5), we can apply the Shoelace Formula:
Area = 1/2 * |(x1y2 + x2y3 + x3y4 + x4y1) - (x2y1 + x3y2 + x4y3 + x1y4)|
Calculating the area:
Area = 1/2 * |((-2 * 2) + (3 * 2) + (7 * -5) + (-2 * -5)) - ((2 * 3) + (2 * 7) + (-5 * -2) + (-2 * 2))|
Area = 1/2 * |(-4 + 6 - 35 + 10) - (6 + 14 + 10 - 4)|
Area = 1/2 * |(-23) - (26)|
Area = 1/2 * |-23 - 26|
Area = 1/2 * |-49|
Area = 1/2 * 49
Area = 24.5
Therefore, the area of the polygon is 24.5 square units.
The Shoelace Formula calculates the area of a polygon by taking the sum of the products of the coordinates of consecutive vertices, with one additional product of the last vertex with the first vertex, and subtracting the sum of the products of the coordinates of consecutive vertices in reverse order.
Given the vertices: A(-2, 2), B(3, 2), C(7, -5), and D(-2, -5), we can apply the Shoelace Formula:
Area = 1/2 * |(x1y2 + x2y3 + x3y4 + x4y1) - (x2y1 + x3y2 + x4y3 + x1y4)|
Calculating the area:
Area = 1/2 * |((-2 * 2) + (3 * 2) + (7 * -5) + (-2 * -5)) - ((2 * 3) + (2 * 7) + (-5 * -2) + (-2 * 2))|
Area = 1/2 * |(-4 + 6 - 35 + 10) - (6 + 14 + 10 - 4)|
Area = 1/2 * |(-23) - (26)|
Area = 1/2 * |-23 - 26|
Area = 1/2 * |-49|
Area = 1/2 * 49
Area = 24.5
Therefore, the area of the polygon is 24.5 square units.
Answer: 24.5 square units.