Question

Four points, A, B, C, and D, have the following coordinates: A(0.75, 0.81) B(0.75, -0.65) C(-1.22, -0.65) D(-1.22, 0.81) What is the area of quadrilateral ABCD, to the nearest hundredth of a square unit? a) 1.44 square units b) 2.88 square units c) 3.00 square units d) 3.24 square units

Answer 1

The area of rectangle ABCD with given coordinates is calculated by multiplying the length of two adjacent sides, resulting in approximately 2.88 square units.

Step-by-step explanation:

The quadrilateral ABCD formed by points A(0.75, 0.81), B(0.75, -0.65), C(-1.22, -0.65), and D(-1.22, 0.81) is a rectangle. The sides parallel to the x-axis are AD and BC, and the sides parallel to the y-axis are AB and CD. To find the area of this rectangle, we calculate the length of one side parallel to the x-axis and one side parallel to the y-axis and then multiply them together.

The length of AD (or BC) can be found by calculating the difference in the x-coordinates of points A and D (or C and B), which is |0.75 - (-1.22)| = 1.97 units. The length of AB (or CD) is found by calculating the difference in the y-coordinates, which is |0.81 - (-0.65)| = 1.46 units.

The area of the rectangle is the product of these two sides, which is 1.97 × 1.46, which equals approximately 2.88 square units.