Question

What is the area of the polygon in square units?

A four-quadrant graph with an irregular polygon with vertices at negative four comma eight, five comma eight, five comma two, nine comma two, twelve comma negative six, and negative four comma negative six.

Answer 1

To find the area of the irregular polygon in the four-quadrant graph, you can break it down into simpler shapes. Split the polygon into a rectangle and two triangles. Calculate the areas of these shapes and add them together for the total area of the polygon.

Step-by-step explanation:

To find the area of the irregular polygon in the four-quadrant graph, we can break it down into simpler shapes and calculate their individual areas.

We can split the polygon into a rectangle and two triangles. The rectangle has a length of 17 units (12-(-4)) and a width of 8 units (8-(-6)). The area of the rectangle is therefore 17 * 8 = 136 square units.

One of the triangles has a base of 4 units (5-(-4)) and a height of 6 units (8-2). The area of the triangle is 0.5 * base * height = 0.5 * 4 * 6 = 12 square units.

The other triangle has a base of 3 units (9-6) and a height of 8 units (2-(-6)). The area of this triangle is also 12 square units.

The total area of the polygon is the sum of the areas of the rectangle and the two triangles, which is 136 + 12 + 12 = 160 square units.