Area
of a Kite
Problem: Find an equation that
relates the area of a kite to its diagonals.
Solution: First, lets get a
definition for a "kite."
Quadrilateral with two pairs of
adjacent equal sides. The geometry of this figure follows from
the fact that it has one axis of symmetry.
(Reference: http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0035954.html)
We can label a similar
kite to the one above in the following way:
Next, I found an equation
for half of the kite by separating it by its axis of symmetry.
Because it is symmetrical, we know that the area of one half of
the kite will equal the area of the other half.
The area of a triangle
is 1/2(bh). The base of the blue triangle is the diagonal d1.
Because of the kite's symmetrical properties, the height of the
blue diagonal is equal to half the length of diagonal d2,
or d2/2.
Therefore, the area
of the blue triangle is
So to obtain the area
of the kite, we can double this value.
Therefore, the area
of a kite in relation to its diagonals equals:
Reference: Project
INTERMATH
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