Using complete sentences, explain how the formula for the area of kite PQRS is derived.

Question

anonymous · Answer

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jack1 · Answer

area = 1/2 x d1 x d2
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jack1 · Answer

if you doubled it, it would equal a rectangle, observe:

anonymous · Answer

I know what the area is, because the kite is cut into two triangles: QPS and QRS. I just can't figure out how to explain in paragraph form.

jack1 · Answer

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jack1 · Answer

why not cut it into 4 triangles
reflective geometry would indicate that a = reflection of a, b = reflection of b, ...etc

anonymous · Answer

Well it can be cut into four, because of the bisectors. I only thought to cut it into 2, for simple terms.

jack1 · Answer

as area of rect = L x W, 
area of kite = 1/2 area of rect
= 1/2 L x W

anonymous · Answer

So, how would I go about answering the question? The formula for kite PQRS is derived from... (the area of the 2 or 4 triangles it is composed of) ?

jack1 · Answer

split it up:
if the cross pieces of d1 and d2 are rightangles (must be for a kite, otherwise it wont fly)
therefore
triangle a doubled = a rectangle
as d1 bisects d2 perfectly
using parallellogram theory:
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