Show that the area of a kite is half the product of its diagonals. Show this:

(A) using algebra, and

(B) using geometry.

Let the diagonals of the kite be $d_1$ and $d_2$.

(A) Algebraic method

The diagonals of a kite are perpendicular, and one diagonal bisects the other.

So, the kite is divided into 4 right triangles.

Adding the areas of all four triangles gives:

Area of kite $= \frac{1}{2} d_{1}d_{2}$

(B) Geometrical method

Draw both diagonals of the kite.

The diagonals divide the kite into four right triangles.

Combine the triangles pairwise to form a rectangle having:

length $= d_{1}$

breadth $= \frac{d_2}{2}$

Area of rectangle: $d_{1} \times \frac{d_{2}}{2}$

Therefore,

Area of kite $= \frac{1}{2} d_{1}d_{2}$