Question

Look at the kite PQRS shown below.

A kite QPSR has PR and QS as its two diagonals. The length of PR is equal to d2 and the length of QS is equal to d1.

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

Answer 1

?????

Answer 2

Yo man, this is a proof, it's long to type.

Answer 3

Anyway...

Answer 4

oh ok..

Answer 5

The diagonals of kites bisect each other so I'm going to call length d2=x and d1=y
Snce it's bisected, the two halves of d2 will equal each other. Now, you have triangle QPS and triangle QRS. Next you apply the formula for a triangle.

Answer 6

Remember that d2=x has been bisected so when you apply the formula, you have x/2 for your height. Also remember that the area of a triangle is \[{1\over 2} \times b \times h\]

Answer 7

b=y and h=x/2
You apply the formula for both triangles and since you have 2, you add them.

Answer 8

umm...idk im confused..but ill try to figure it out i guess..

Answer 9

Ok, this is going to take a bit of time to write.

Answer 10

ok ill be back in a secong

Answer 11

ok im back now

Answer 12

?? thats taking an awfull long time to type..it just has to be simple and to the point...

Answer 13

\[{\frac 1 2} \times b \times h ={\frac 1 2} \times y \times {\frac x 2}\]
That is the area for one triangle: lets say QPS.
We do the same thing for triangle QRS.
\[{\frac 1 2} \times b \times h ={\frac 1 2} \times y \times {\frac x 2}\]
Next, we add them: area of triangle QPS and area of triangle QRS
\[{\frac 1 2} \times y \times {\frac x 2}\]
\[({\frac 1 2} \times y \times {\frac x 2})+({\frac 1 2} \times y \times {\frac x 2})\]
So we get \[{xy\over 4} +{xy\over 4}={{2xy}\over 4}={{xy}\over 2}\]
Where x is the diagonal d2 and y is the diagonal d1.

Answer 14

The diagonals of kites bisect each other so I'm going to call length d2=x and d1=y Since it's bisected, the two halves of d2 will equal each other. Now, you have triangle QPS and triangle QRS. Next you apply the formula for a triangle.
Area of a triangle is 1/2BH. and D2 is bisected so when the formula is applied x/2 would be the height, and b=y. so 1/2*x/2*y would be the area for 1 triangle but we have 2. So it would be 1*2x/2*2y?...

Answer 15

Well, I didn't know how detailed you needed it to be...

Answer 16

oh ok lol

Answer 17

i actually have one more but im gonna guess. Thanks for all of your help!