What is the area of this figure? Enter your answer in the box. unitsĀ² An irregular heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair negative 4 comma 5 end ordered pair, begin ordered pair negative 2 comma 3 end ordered pair, begin ordered pair 3 comma 4 end ordered pair, begin ordered pair 4 comma 3 end ordered pair, begin ordered pair 4 comma negative 3 end ordered pair, and begin ordered pair negative 3 comma negative 3 end ordered pair.

Guest Mar 3, 2017

#1**+5 **

We can use something called "Pick's Theorem to solve this.....

The theorem says that as long as the vertices of a figure lie on integer coordinates .....like yours....we can calculate the area as :

B/2 + I - 1

Where B is the number of boundary points [" boundary points" are defined as the number of time the edges of the figure intersect integer coordinates...i,e.....the intersection of the grid lines ]

And I is the number of interior points [ again....these are the number of interior points that lie on integer coordinates]

We have 14 boundary points and 27 interior points

So.....the area = 14/2 + 27 - 1 = 7 + 27 - 1 = 34 - 1 = 33 sq units

Heres's a pic :

CPhill
Mar 3, 2017