10.4 Area of Kites and Rhombuses

The area of a kite can be visualized as composed of triangles. Diagonals are perpendicular, and one bisects the other. The total area can be derived from the triangles: two small triangles (KIP, KEP) and two lower triangles (TIP, TEP). Areas for these triangles are calculated as follows:

• Area of triangle KIP: ext{Area} = rac{1}{2} imes ext{base (IP)} imes ext{height (KP)}

• Area for TIP: ext{Area} = rac{1}{2} imes ext{base (IP)} imes ext{height (PT)}

• Combined area gives: ext{Area} = IP imes (KP + PT)

Each of the larger triangles (KIE, TIE) also has similar area calculations leading to:
ext{Area} = rac{1}{2} imes ext{diagonal 1} imes ext{diagonal 2}

This confirms the area formula for both kites and rhombuses as: ext{Area} = rac{1}{2} imes d1 imes d2 .

Example Problem: For diagonals of 9 m and 14 m:
ext{Area} = rac{1}{2} imes 9 imes 14 = 63 ext{ m}² .

Rhombus area follows a similar approach: Perimeter of 20 cm with longer diagonal 8 cm yields an area of $$ 24 ext{ cm