Question

The coordinates of the vertices of a regular polygon are given. Find the area of the polygon to the nearest tenth.

Answer 1

Answer:

The area is equal to $8\ units^{2}$

Step-by-step explanation:

we have

A(0, 0), B(2, -2), C(0, -4), D(-2, -2)

Plot the figure

The figure is a square (remember that a regular polygon has equal sides and equal internal angles)

see the attached figure

The area of the square is

$A=AB^{2}$

Find the distance AB

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}$

$AB=\sqrt{(-2)^{2}+(2)^{2}}$

$AB=\sqrt{8}$

$AB=2\sqrt{2}\ units$

Find the area of the square

$A=(2\sqrt{2})^{2}$

$A=8\ units^{2}$