What is the area of the regular hexagon shown below? Answer in complete sentences and include all relevant calculations.

6381.4 cm²

Step-by-step explanation:

Applying,

A = n/2(a×h) Equation 1

Where A = Area of the regular polygon, n = number of sides of the polygon, a = length of one side of the polygon, h = length of the apothem

But,

a = 2htan∅ Equation 2

Where ∅ = angle substands at the center by the regular polygon.

∅ = 360/n Equation 3

Substitute equation 3 into equation 2

a = 2htan(360/n) Equation 4

Substitute equation 4 into equation 1

A = n/2[2htan(360/n)×h) Equation 5

From the question,

Given: n = 6 side, h = 24.78 cm

Substitute these values into equation 5

A = 6/2[24.78×24.78×2×tan(360/6)]

A = 3[24.78×(24.78×2×tan60°)]

A = 6381.4 cm²

1.000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(-3+x)=0

STEP1:

Equation of a Straight Line

1.1     Solve   y-x+3  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on a Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y-axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-x+3 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -3/1 so this line "cuts" the y axis at y=-3.00000

 y-intercept = -3/1  = -3.00000

Calculate the X-Intercept :

When y = 0 the value of x is 3/1 Our line therefore "cuts" the x-axis at x= 3.00000

 x-intercept = 3/1  =  3.00000

Calculate the Slope :

The slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.000 and for x=2.000, the value of y is -1.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.000 - (-3.000) = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  2.000/2.000 =  1.000

Geometric figure: Straight Line

Slope = 2.000/2.000 = 1.000

x-intercept = 3/1 = 3.00000

y-intercept = -3/1 = -3.00000

Hope this helps!

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