The Area of the polygon 6 square units.
In geometry, a polygon is a closed, two-dimensional shape that is made up of three or more line segments. A triangle is a polygon with three sides and three angles.
A polygon can be decomposed into smaller polygons, and a triangle is the simplest type of polygon.
The polygon shown in the image is a quadrilateral, which is a polygon with four sides. It can be decomposed into two triangles, ABC and ADC, by drawing a diagonal line from point A to point C.
This diagonal line divides the quadrilateral into two congruent triangles, meaning that they have the same size and shape.
The area of a triangle can be calculated using the following formula:
Area of triangle = 1/2 * base * height
where the base is the length of one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
To find the total area of the shaded polygon, we need to find the areas of triangles ABC and ADC and then add them together.
The base of triangle ABC is 4 units and the height is 3 units, so the area of triangle ABC is 6 square units. The base of triangle ADC is 3 units and the height is 4 units, so the area of triangle ADC is also 6 square units.
Therefore, the total area of the shaded polygon is 6 square units.