# Geometry

Find the area of a hexagon with the indicated apothem:

6 sqr root 3

108 sqr root 3 in.^2
432 sqr root 3 in.^2
96 sqr root 3 in.^2
216 sqr root 3 in.^2

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1. Area = 1/2 x perimeter x apothem
= 1/2 (6s)(6√3)

once you tell me what the side (s) of the hexagon is, we an finish the question

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posted by Reiny
2. They don't tell you the sides, the apothem is all they give you.

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3. So, I guess we can't find the area, since we need the side

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posted by Reiny
4. Hm, I mean, there has to be a way to figure the side out with just the apothem. Problem is that I'm not good with formulas or square roots.
First off, what is the apothem? What is 6 square root 3?

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5. ok, ok

I stand corrected, there is a way, we have an angle.
The apothem is the distance from the centre to the midpoint of a side

Let's look at one of the triangles of the hexagon.
It has a central angle of 60
so in a right-angled triangle formed by the apothem and half the base, I'll call it x
x/6√3 = tan 30
x = 6√3tan30
base = 12√3tan30= 12

area = Area = 1/2 x perimeter x apothem
= (1/2)(72)(6√3)
= 216√3 units^2

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posted by Reiny
6. Unit 5: Area
Lesson 4: Perimeters and Areas of Similar Figures
Perimeters and Areas of Similar Figures Quiz
1) A - 14.04cm^2
2) A - 34cm^2
3) A - 144.5cm^2
4) D - 12cm
5) A - 144 + 72squareroot3
6) B - 15.9ft^2
7) D - 72squareroot3
8) B - 73.5squareroot3cm^2
9) C - 5 : 4 and 25 : 16
10) C - 3181m^2
11) A - \$81.25
12) D - the area would not change
13) D - 216squareroot3in^2
100%

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7. Raaayleeee is right

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8. You are 100% correct! Thanks!!

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