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Alexeev081 [22]
3 years ago
15

Two similar regular hexagons have a common center. If each side of the big hexagon is twice the side of the small one and the ar

ea of the small hexagon is 3 sq. in, what is the area of the big hexagon?
Mathematics
1 answer:
Anna71 [15]3 years ago
7 0
To determine any area of a shape we need to know the formula for the area of that particular shape which is for a regular hexagon is 

Area of hexagon = (3 √3) a^2 / 2
 where a is the length of the side of the hexagon
So, first, we determine the length of the side of the smaller hexagon from the given area.

3 in^2 = (3 √3) a^2 / 2
6 in^2 = (3 √3) a^2 
a^2 = 2 √3 / 3
a = 1.0746 in

The length of the side of the bigger hexagon is twice that of the smaller so,
A = 2a = 2 (1.0746 in ) = 2.1491 in

Area of the bigger hexagon =  (3 √3) a^2 / 2
                                            = (3 √3) 2.1491^2 / 2                                            = 12 in^2
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32 - 8 = 24. This means that there were 24 winning games and 8 losing games.

24 multiplied by 5/8 = 15. Katy was a catcher in 15 of the winning games.

8 multiplied by 1/4 = 2. Katy was a catcher in 2 of the losing games.

In total, Katy was a catcher in 17 of the games.

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A deck has side lengths 16 feet, 18 feet, 16 feet, 8 feet, and 12 feet.
BigorU [14]

The area of the deck is 413 square feet

<h3>How to determine the area of the proposed deck?</h3>

Start by calculating the area of the outer rectangle using:

Area = Length * Width

This gives

Area1 = (18 + 12) * (16 + 8)

Area1 = 720

Next, calculate the area of the inner rectangle using:

Area = Length * Width

This gives

Area2 = 16 * (18 + 8)

Area2 = 416

Subtract these areas

A1 = Area1 - Area2

A1 = 720 - 416

A1 = 304

Next, calculate the area of the outer semicircle using:

Area = 0.5πR²

This gives

Area1 = 0.5 * 3 * (12-1)²

Area1 = 181.5

Next, calculate the area of the inner semicircle using:

Area = 0.5πr²

This gives

Area2 = 0.5 * 3 * (7)²

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Subtract these areas

A2 = Area1 - Area2

A2 = 181.5 - 73.5

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Add A1 and A2

A = 304 + 108

Evaluate the sum

A = 412

Hence, the area of the deck is 413 square feet

Read more about areas at:

brainly.com/question/24487155

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