To find the area of an octagon, we can divide it into two triangles, so the area of the kite is (1/2)(6 meters)(3 meters) = 9 square meters.
Divide the kite into two right triangles, with the diagonal of the kite forming the hypotenuse of each triangle.
The area of a triangle is equal to one-half base times height. In each right triangle, one leg is half the length of the kite’s vertical side, and the other leg is half the length of the kite’s horizontal side.
Therefore, the area of each triangle is (1/2)(vertical side/2)(horizontal side/2) = (1/4)(vertical side)(horizontal side).
Since the area of the kite is the sum of the areas of the two triangles, the area of the kite is 2[(1/4)(vertical side)(horizontal side)] = (1/2)(vertical side)(horizontal side).
In the image, the vertical side is 6 meters and the horizontal side is 3 meters, so the area of the kite is (1/2)(6 meters)(3 meters) = 9 square meters.