Mrs. Cashner

Geometry 10

9 May 2013

All You Need To Know: Chapters 7 and 11 Hello my friend I hope you are now well recovered from your cold. Don’t worry you weren’t the only one who was absent that day. I am also getting sick, but I don’t want to miss school, I know you will probably help me get caught up with Geometry if I get sick .While you were out you missed parts of chapter 7 and 11. We talked about special rights triangles, trigonometry ratios, and many other things. Throughout this paper, I will be explaining you how the process is of finding the area of a hexagon. Let’s say for instance that we have to find the area of a regular hexagon with a radius of 7centemeters. You can solve this problem by using the special right triangle knowledge and you will be using three formulas with that which are H=2*SL, LL=SL*√3, and ½ SAN. The first thing you will need to do is to make a triangle inside the hexagon with the Hypotenuse of 7. After that you will first use the formula of H=2*SL, you will plug in the 7 on the “H” place to equal 2 times the SL. To solve for the SL you have to divide the 2 on both sides and at the end 7 divided by 2 equals 3.5, so that means that SL=3.5. After that you move to the second formula of LL=SL*√3, you will plug in the 3.5 on the SL place, so that your formula can be LL=3.5*√3, after you multiply 3.5*√3, LL=6.06. The last formula is ½ SAN, you will keep the ½, “s” stands for side length which will be 7, “a” stands for apothem, and “n” stands for number of sides, in this case it will be 6 because a hexagon has 6 sides. Your formula set up will be ½(7) (6.06) (6) and after multiplying your answer will be 127.26.

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H=2*SL

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LL=SL*√3

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½ SAN

7=2*SL

3.5=SL

LL=3.5*√3 1/2 SAN

6 sides on the hexagon

LL=6.06 ½ (7) (6.06) (6)= 127.26

You can also solve this problem by using the Trigonometric Ratio Knowledge. We will keep our example of trying to find the area of a regular hexagon with a radius of 7centemeters. The first thing you will need to do is to make a triangle inside the hexagon with the Hypotenuse of 7. To figure out the measurement of the triangle will be, you will divide 360/6=60/2=30. The measurement of the triangle will be 30, 60, and 90 degrees. To find the missing lengths you will use SOH, CAH, and TOA. You will find the opposite of 30 degrees, the adjacent, and the hypotenuse. To find the apothem you will use the CAH, which it will be the adjacent of “x” and hypotenuse “7” of 30 degrees. Your formula of the Trigonometric Ratio Knowledge will be COS30=x/7. To simplify this equation you will multiply the 7 on both sides and your final answer will be x=6.06 for the hypotenuse. At the end you will again use ½ SAN, your formula set up will be ½(7) (6.06) (6) and after multiplying your answer will be 127.26.

7*COS 30= x 7

6.06=x

7 SOH CAH TOA

=127.26

63.63+63.63

6.06 63.63

2

14+7

2

b1+b2 h 6.06

7

14 You can also solve this problem by braking down the hexagon into 2 separate trapezoids. We will keep our example of trying to find the area of a regular hexagon with a radius of