# Geometry

posted by SkatingDJ

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

1. Reiny

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

2. SkatingDJ

They don't tell you the sides, the apothem is all they give you.

3. Reiny

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

4. SkatingDJ

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?

5. Reiny

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

6. Raaayleeee

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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