Answer:
The area of ABCD is 24 units²
Explanation:
* Lets explain how to solve the problem
- All the point in a vertical line have the same x-coordinates
- The length of the vertical line is y2 - y1
- All the point in a horizontal line have the same y-coordinates
- The length of the horizontal line is x2 - x1
- The horizontal and the vertical lines are perpendicular to each other
- The trapezoid has two parallel bases not equal in length and the other
two sides are nonparallel sides
- The area of the trapezoid = 1/2 (sum of the two // bases) × height
* Lets solve the problem
∵ ABCD is a quadrilateral
∵ A = (-2 , 3) , B = (4 , 3) , C = (4 , -2) , D = (-2 , 0)
∵ Side AD has same x-coordinates in A and D (-2)
∴ AD is vertical side
∴ AD = 3 - 0 = 3
∵ Side BC has same x-coordinates in B and C (4)
∴ BC is vertical side
∴ BC = 3 - (-2) = 3 + 2 = 5
∵ AD and BC are vertical lines
∴ AD // BC
∵ Side AB has same y-coordinates in A and B (3)
∴ AB is horizontal side
∴ AB = 4 - (-2) = 4 + 2 = 6
∵ The horizontal and the vertical lines are perpendicular to each other
∴ AB is perpendicular on AD and BC
∵ The side CD is not vertical or horizontal
∴ ABCD has only two parallel sides AD and BC
∵ AD ≠ BC
∴ ABCD is a trapezoid
∵ The two parallel bases are AD and BC
∵ Its height is AB
∵ AD = 3 , BC = 5 , AB = 6
∴ Its area = 1/2 (3 + 5) × 6 = 1/2 (8) × 6 = 4 × 6 = 24 units²
* The area of ABCD is 24 units²