Question

By what factor does the area change if one diagonal is doubled? Explain.

Answer 1

the kite, which looks more like a rhombus but being called a kite, will look like the one in the picture below.

now, as you see in the picture, the kite is really 4 congruent triangles, each with a base of 2.5 and a height of 5, so their area is

$\bf \stackrel{\textit{area of one triangle}}{\cfrac{1}{2}(2.5)(5)}\implies 6.25\qquad \qquad \stackrel{\textit{area of all four triangles}}{4\left[ \cfrac{1}{2}(2.5)(5) \right]}\implies 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doubling the base or height}}{4\left[ \cfrac{1}{2}(2.5)(5)\underline{(2)} \right]}\implies \stackrel{\textit{the area is twice as much as the original}}{\underline{(2)}~~\left[ 4\left[ \cfrac{1}{2}(2.5)(5) \right] \right]}$

Answer 2

The area of deltoid is defined by formula:

$A=\dfrac{e\cdot f}{2}$

Where e and f are diagonals.

If you were to double the size of either one. Let's say f. You would result with:

$A=\dfrac{e\cdot2f}{2}=e\cdot f$

Which means if either of diagonals double in length the area of deltoid will be twice as big as it was before.

Hope this helps.

r3t40