Find the area of the shaded region. Round your answer to the nearest hundredth,
12

79.2

Step-by-step explanation:

First of all we need to find the Apothem of the polygon. The apothem is the same as the inner radius but it is not the radius of the outer circle. If it was an innercircle, the apothem would be the same but this is the case of on outer circle.

, where s = 12 and n (number of sides) = 5

Substituting the numbers in we would get a = 8.26.

Now the area of a polygon = , where a is the apothem (we just got it and p and is the perimeter of the polygon.

This is an equal side polygon, this means all of the sides are 12 in length and we have 5 sides, this makes p = 12 * 5 = 60

Area =

Now, all we need to do is the find the area of the circle and subtract it from that number. However, we don't know the radius.

To find the radius, we use this equation:

, we know a is 8.26 and n = 5,

substituting, we will end up with 10.2

Area of circle = , where r is 10.2

Area of circle = 327.

Area of shaded region = Area of the circle - polygon

Area = 327 - 247.8= 79.2

Wow, thats a great question. Had to look up some formulas too.

Hope this helps.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

3 is greater then both of those numbers