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3 years ago

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

1 answer:

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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Chef Rita Is cooking for a Sunday brunch.She knows that 22 pancakes can feed 8 people.She is wondering how many people she can f

AlexFokin [52]

Answer:

Chef Rita can feed 20 people with 55 pancakes.

Step-by-step explanation:

We can solve this problem using equivalent ratios. Since we know that Chef Rita can feed 8 people with 22 pancakes, we can set up the ratio:

$\frac{22pancakes}{8people}=\frac{22}{8}$

To solve how many people she would be able to feed with 55 pancakes, we can set ratios equal to each other and solve for 'x' which is the number of people.

$\frac{22}{8}=\frac{55}{x}$

We can see what factor we multiply 22 by to get 55 and then we multiply the denominator by the same factor to get our equivalent ratio. 55 ÷ 22 = 2.5. So, 8 x 2.5 = 20 people.

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3 years ago

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Evaluate 4x^2 y^-3 for x=3 and y=-2

Doss [256]

Answer:

36 and -1/8

Step-by-step explanation:

x^2 = 3^2 = 9 * 4 = 36

y^-3 = (-2)^-3 = -1/8

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2 years ago

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The tables show the battery lives (in hours) of two brands of laptops. Which brand's battery lives are more spread out? Explain

GalinKa [24]

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2 years ago

Please help! if you answer it correctly, i'll give brainliest!!

lozanna [386]

Answer:

9 cm

Step-by-step explanation:

$\sqrt[3]{729}$

$=\sqrt[3]{9*9*9}$

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3 years ago

Anuja is baking cookies for her slumber party this weekend. She has one supersize package of Sugar Sprinkles and one supersize p

olga_2 [115]

There are some missing details in the question. I found a similar question with some addition of details as follows:

The Sugar Sprinkles package contained 3/4 of a cup of the mix that needs to be mixed with 2 2/5 cups of flour, 2 1/4 cups of brown sugar, 3 3/8 and cups of water. The directions indicate to use 0.1125 of a cup of dough to make one cookie and 1 batch should make a total of Sugar Sprinkles cookies.

The Chocolate Turtle package contained 0.875 of a cup of the mix that needs to be mixed with 3.25 cups of flour, 2.5 cups of brown sugar, and 3.75 cups of water. The directions indicate to use 1/8 of a cup of dough to make one cookie and 1 batch should make a total of Chocolate Turtle cookies. The difference in the number of cookies of each type is _____

Answer:

Difference in number of cookies is 1

Step-by-step explanation:

This question is quite a tricky one. You have to be careful when answering it.

For sugar sprinklers, it contains 3/4 of a cup of the dough. For every 0.1125 of a cup, 1 cookie can be made.

So, 3/4 ÷ 0.1125

= 0.75 ÷ 0.1125

= 6.66667

Hence the most can be made is 6.

Note that we do not use the other volume because 0.1125 cup of a dough is the amount of cup from the original mix

The same applies to chocolate turtle cookies. It contains 0.875 of a cup. For every 1/8 of a cup can make 1 cookie.

0.875 ÷ 1/8 = 7

So the difference in the number of cookies is 7 - 6 = 1

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3 years ago