Question

the area of the polygon with verticles at (1,3)(7,3)(7,7)and (4,7)

Answer 1

Call the polygon (trapezoid) ABCD, taking the points in alphabetical order.

AB is horizontal because they share the same y-coordinate, similarly DC is horizontal.

The length of AB is 7-1=6 units; the length of DC is 7-4=3 units.

BC share the same x-coordinate, making BC vertical and perpendicular to AB. The length of BC=7-3=4, which is the height of the trapezoid ABCD.

The area of a trapezoid is half the sum of the parallel sides times the height. Therefore:

The area=½(AB+DC)×BC=½(6+3)×4=18 square units.

The same result can be obtained by summing the area of a 3 by 4 rectangle (12 square units) and the area of a triangle with height 4 and base 3 (6 square units): 12+6=18 square units.