8. Determine the most precise name for the quadrilateral & find the area. (2 points)

The object is a rectangle, I just need the area of it

coordinates: A(3,4), B(8,1), C(2,-9), D(-3,-6)

1 answer

The most precise name for this quadrilateral is a rectangle. To find the area of a rectangle, we can use the formula:

Area = length × width

To find the length and width of the rectangle, we can use the distance formula between the given coordinates:

AB = √((8-3)^2 + (1-4)^2) = √(5^2 + (-3)^2) = √(25 + 9) = √34
BC = √((2-8)^2 + (-9-1)^2) = √((-6)^2 + (-10)^2) = √(36 + 100) = √136
CD = √((-3-2)^2 + (-6+9)^2) = √((-5)^2 + 3^2) = √(25 + 9) = √34
DA = √((3+3)^2 + (4+6)^2) = √(6^2 + 10^2) = √(36 + 100) = √136

The diagonals are equal in a rectangle, so AB = CD and BC = DA. So, we can take AB and BC as the length and width of the rectangle:

Area = √34 × √136 ≈ 18.44 × 11.66 ≈ 215.15

Therefore, the area of the rectangle is approximately 215.15 square units.