Question

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

A (2,2), B (9,2), C (9,-3), D (2, -3)
A= square units

HELP

Answer 1

A = 35 square units

Explanation:

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

d =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Length of the segment between A(2, 2) and B(9, 2) =
`√((9-2)^2+(2-2)^2)`

= 7 units

Length of the segment between B(9, 2) and C(9, -3) =
`√((9-9)^2+(2+3)^2)`

= 5 units

Length of the segment between C(9, -3) and D(2, -3) =
`√((9-2)^2+(-3+3)^2)`

= 7 units

Length of the segment between A(2, 2) and D(2, -3) =
`√((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