Question

Find the area of the polygon.

3, 1, 1, 7.2, 6

___square units

Answer 1

To find the area of a polygon, we need to break it down into triangles and then calculate the area of each individual triangle.

The polygon with the given vertices (3, 1, 1, 7.2, 6) can be divided into two triangles:
1. (3, 1, 1)
2. (1, 7.2, 6)

First, let's find the area of Triangle 1:
Base = 3 - 1 = 2 units
Height = 1 unit
Area = 1/2 * Base * Height = 1/2 * 2 * 1 = 1 square unit

Next, let's find the area of Triangle 2:
Base = 6 - 1 = 5 units
Height = 7.2 - 1 = 6.2 units
Area = 1/2 * Base * Height = 1/2 * 5 * 6.2 = 15.5 square units

Now, add the areas of Triangle 1 and Triangle 2 to find the total area:
Total Area = Area of Triangle 1 + Area of Triangle 2
Total Area = 1 + 15.5 = 16.5 square units

Therefore, the area of the given polygon is 16.5 square units.