Diagonals d1 and d2 cross perpendicularly. (i) Algebraically, the kite splits into two triangles on base d1 with heights summing to d2, giving area (1/2)d1d2. (ii) Geometrically, enclosing it in a d1 x d2 rectangle doubles its area.
Show that the area of a kite is half the product of its diagonals. Show this: (i) using algebra and (ii) using geometry.
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In a kite, diagonals d1 and d2 are perpendicular and one diagonal (say d1) bisects the other (d2 = h1 + h2).
(i) Using algebra:
The main diagonal d1 divides the kite into two triangles with common base d1 and perpendicular heights h1 and h2.
Total Area = (1/2)d1h1 + (1/2)d1h2 = (1/2)d1(h1 + h2) = (1/2)d1d2.
(ii) Using geometry:
Draw lines through the vertices parallel to both diagonals to form a bounding rectangle of dimensions d1 and d2 (area = d1d2). Each of the four corner right triangles outside the kite is congruent to an adjacent right triangle inside the kite. Thus, the kite fills exactly half the rectangle:
Area = (1/2)d1d2.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/