What is the edge length of a hexagon with a circle radius of 22 inches?

Just a little over 53.3 gallons

Well, if you know the side 'a' of each hexagon it is just a*(30 - 4) = 26a

If you know the diameter of the circle enclosing the hexagon then
a = D/2 as radius = a

(pi)R squared (Fixya won't let me use the sign for Pi)

Area of a circle=pi*radius^2 or pi times radius times radius

example: suppose the radius of a circle is 10 inches, then the Area of the circle would be pi times 10 times 10 or 100*pi

pi represents the circumference (distance around) of a circle / diameter and for any circle is constantly the same number which is approximately 3.14

so in my example 100*pi=100*3.14 or 314 square inches

If you would like to know the circumference of a 15" diameter circle this is the formula:
circumference = radius x 2 x pi
circumference = diameter x pi

in our case:
circumference = 15" x 3,14
circumference = 47 ,1" (that's 119,634 cm)

I will not try to guess what that diameter represents, so I will give you all mensuration formulas for the area of a regular polygon.
s is the measure of the side, r the radius of the inscribed circle, R the radius of the circumscribed circle, and n the number of sides.
If the angle unit in your calculator is the degree, use 180 instead of Pi. Use the formulas with PI if angle unit is set to radians.
In the formulas on the last line of the display screen (the formulas with sine functions) the radius r should be R (circumscribed circle radius). cot is the reciprocal of the tangent function (cot(x)=1/tan(x) )

The length of your equipment, even more than the scale of the model, is the most important factor in setting a minimum radius. The list below includes conventionally accepted minimums for each of the major scales.

• Z Scale: 195 mm
• N Scale: 9 3/4 inches
• HO Scale: 15-22 inches
• HOn3 Scale: 15 inches (narrow gauge)
• S Scale: 20 - 30 inches
• O Scale ("Toy"): 13.5 inches
• O Scale ("Scale"): 72 inches
• On3 Scale: 36 inches
• G Scale: 24-44 inches

Well it depends. If the hexagon is irregular (sides are not equal) there is no formula to calculate the sides as they can have arbitrary values. You must measure them.
If the hexagon is regular you may be able to relate the measure of a side to the radius of the circle in which it is inscribed. If you have the radius of the circle, the side is equal to the radius. If you have the value of perimeter you divide that value by 6.
There is also a formula that relates the area of the hexagon to the measure of the side s. The formula is Area=(6/4)(s^2)cot(PI/6), where cot is the cotangent function, its angle is in radian. In degrees Pi/6 is 30 degrees.

You can not do it unless you know the measure of the central angle sustending (supporting) the arc. If the angle is known, you use the proportionality relation that follows:
If angle is in degrees
(length of arc) / circumference=(measure of central angle sustending arc)/360.
Here the circumference is 2*PI*radius.

If angle is in radians , the relation is somewhat simpler,
arc length= (radius length)* (angle measure in radians)
It is clear that in the last relation, the unit for the arc length is the same as the unit for the radius.

The diameter of the circle is the diagonal of the rectangle use Pythagoras this rectangle is a made from two 3,4,5 triangles, so the diameter is 5cm, the radius will be 2.5cm don't forget the BODMAS ordering rule (Brackets of Division Multiplication Addition and Subtraction) Also rounding to 2 decimal places. This solution is based on all four corners of the rectangle touching the circumference of the circle.

Area of a circle is P (22/7) i x Radius (squared ^2) ====> 22/7 x 2.5cm ^ 2 ====> 22/7 x 6.25cm

TOTAL AREA of CIRCLE = 19.64 cm^2

Area of the rectangle is length x width ====> 4 cm x 3 cm

TOTAL AREA of RECTANGLE = 12 cm ^2

The remaining portion is the circle area minus the rectangle 19.64-12 = 7.64 cm^2


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what class are you in? Is this your home work? Anyway, You should know that
Circumference = 2 x pie x radius therefore radius - circumference / 2 x pie in this case radius = 30 x 7 / 2 x 22 = 210 / 44 Now you can calculate that fraction.