Question

In quadrilateral RANK, which is a square, AK and RN intersect at point I. If NR is 18 cm, and it is given that N is equal to 18/R cm, what is the area of square RANK?

Answer 1

To find the area of square RANK, we deduce that each side is
`18` cm by using given values. Squaring this side length gives us the area of the square as
`324 cm²`.

Step-by-step explanation:

In the quadrilateral RANK, which is a square, the diagonals AK and RN intersect at point I, dividing each other into equal halves. Given that NR is 18 cm, which is also the length of each side of the square since all sides in a square are equal.

Furthermore, the measure of N is provided as
`18/R cm`, leading us to the conclusion that R must be equal to
`1`because R multiplied by N equals NR, or
`18`. Hence, R equals
`18` divided by
`18`, which is
`1 cm`.

The area of the square RANK is then calculated by squaring the length of one of its sides.

Therefore,
`Area = NR² = 18cm * 18cm = 324 cm²`.