Question

Find the area A of the polygon with the given vertices.

Answer 1

Answer:

A = 35 square units

Step-by-step explanation:

Formula to calculate the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Length of the segment between A(2, 2) and B(9, 2) = $\sqrt{(9-2)^2+(2-2)^2}$

                                                                                     = 7 units

Length of the segment between B(9, 2) and C(9, -3) = $\sqrt{(9-9)^2+(2+3)^2}$

                                                                                       = 5 units

Length of the segment between C(9, -3) and D(2, -3) = $\sqrt{(9-2)^2+(-3+3)^2}$

                                                                                        = 7 units

Length of the segment between A(2, 2) and D(2, -3) = $\sqrt{(2-2)^2+(2+3)^2}$

                                                                                       = 5 units

Therefore, given polygon is a rectangle.

Area of the rectangle = length × width

                                    = 7 × 5

                                    = 35 square units