Question

quadrilateral abcd is dilated to produce quadrilateral a′b′c′d′ with a scale factor of n. if the area of ABCD is r, what is the area of a’b’c’d’

Answer 1

Answer:

The area of the quadrilateral a'b'c'd' is $r(n^{2})\ units^{2}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> the area of the dilated quadrilateral a'b'c'd'

y----> the area of the original quadrilateral abcd

$z^{2}=\frac{x}{y}$

we have

$z=n$

$y=r\ units^{2}$

substitute the values

$n^{2}=\frac{x}{r}$

$x=r(n^{2})\ units^{2}$ ------> area of the quadrilateral a'b'c'd'