Regular hexagons P and Q are shown. 2 cm
6 cm
Q
P
How do the areas of hexagons Pand compare?
O A The area of Pis 3 times the area of Q.
OB. The area of Pis 9 times the area of 0.
OC. The area of Pis 12 times the area of Q.
OD. The area of Pis 18 times the area of Q.

9514 1404 393

  B.  The area of P is 9 times the area of Q.

Step-by-step explanation:

The areas of similar figures are related by the square of the scale factor of their linear dimensions. The ratio of side lengths is ...

  side of P : side of Q = 6 : 2 = 3 : 1

So, the ratio of areas is ...

  area of P : area of Q = 3² : 1² = 9 : 1

The area of P is 9 times that of Q.

Step-by-step explanation:

One way to do this would be to find the circumference of the entire circle and divide it by 4, considering that the arc measure is 90 degrees

The radius is 1, and the circumference can be found by taking

So, the circumference of this circle is

Now, all we have to do is divide that by four to get our answer