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seraphim [82]
3 years ago
12

A regular hexagon has a perimeter of 120 m. Find its area. Leave your answer in simplest radical form.

Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0
To find the area of any regular shape, its formula is

(1/2) • a • p

Where a is the apothem (a line from the center of a side to the center of the shape) and p is the perimeter.

We have the perimeter: 120

Now to find the apothem. To find it, we’re going to cut any sidelength in half, and the line from that half to the center of the hexagon will form a right triangle. We know the bottom leg (where the shape is) is 10 (since 120/6 = 20, and we cut that in half). All we need is angles. To find the interior angle of any regular shape, we use

(180(n - 2))/n

Plugging in, we get 120 degrees for every side. Since we cut it in half, then the top angle of our right triangle is 60. You know what that means? We’ve just found a 30, 60, 90 triangle.

Using the laws of this special triangle, the length of the apothem is the shortest leg times sqrt(3)

So, 10sqrt(3) is your apothem.

Plug everything in!

(1/2) • a • P

(1/2) • 10sqrt(3) • 120

Your area is 600sqrt(3)
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Help with #2 it has to do with number 1 that is the polygon you need to find the area of it.
Katena32 [7]
Okay, it's the equation to how find area any other way. A=L×W

This means *picture above*

So then you count over each line meaning 1.
This means L=9 and a 1/2. Since its in between the 2 an 3 on the x-axis.
Now for W or width. It equals 3 since you can count 2 lines and one either ends of the polygon is 1/2 each this creates one when added together.

All you do from there is multiply 9 and 3. This should give you A=area.

8 0
3 years ago
identify an equation in the point-slope form for the line parallel to y=1/2 x -7 that passes through (-3,-2)
Mariulka [41]

Answer:

Step-by-step explanation:

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= -3      y_1= -2         m= 1/2(parallel means same slope)

an equation in the point-slope form is : y +2 = 1/2(x+3)

3 0
3 years ago
!!!20 POINTS!!!90 feet per minute. how many hours to walk 3 miles use unit analysis​
Molodets [167]

Answer:33.3

Step-by-step explanation: a mile is 1000×3 so it's 3000/90

6 0
3 years ago
The population of Hillsborough County in Florida in 2010 was 1,229,226 and the land
Kruka [31]

Answer:

About 1205.12352941 people per square mile in 2010

About 1329.36306853 people per square mile in 2015

Explanation:

take population and divide by land area

for 2015 pop do total pop divided by 9.7 plus total pop

6 0
2 years ago
5. It is given that -2,4, a, b and care five consecutive terms of a geometric progression. Find the value of c.
vlada-n [284]

Answer:

c = - 32

Step-by-step explanation:

The common ratio r of the sequence is

r = \frac{a_{2} }{a_{1} } = \frac{4}{-2} = - 2

To find the next term in the sequence multiply the previous term by r

a = 4 × - 2 = - 8

b = - 8 × - 2 = 16

c = 16 × - 2 = - 32

3 0
3 years ago
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