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3 years ago

Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon?

Mathematics

2 answers:

Rasek [7]3 years ago

8 0

Answer

Find out the area of the regular hexagon.

To prove

As given in the question

Hexagon is regular thus it is made up of the six equilateral triangle.

Thus area of the regular hexagon is 6 times the area of a equilateral triangle.

Each side of the regular hexagon measures 8 cm.

Formula

$Area\ of\ hexagon = 6\times \frac{\sqrt{3}a^{2}}{4}$

where a represented the side.

$Area\ of\ hexagon = 6\times \frac{\sqrt{3}\times 8\times 8}{4}$

$Area\ of\ hexagon = 6\times \sqrt{3}\times 8\times 2$

$Area\ of\ hexagon = 96 \sqrt{3}\ unit^{2}$

Therefore the option (a) is correct .

sineoko [7]3 years ago

6 0

A regular hexagon can be split into 6 congruent equilateral triangles.
the area of an equilateral triangle is √3*s²/4, where s is the side length
Area of the hexagon
= 6*√3*8²/4
= 96√3 square centimeters

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3 years ago

A certain hybrid car has a mileage rating of 57 miles per gallon. if the car makes a trip of 293 miles, how many gallons of gaso

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3 years ago

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Rufina [12.5K]

Answer: 1 .Thus for a graph to have an Euler circuit, all vertices must have even degree. The converse is also true: if all the vertices of a graph have even degree, then the graph has an Euler circuit, and if there are exactly two vertices with odd degree, the graph has an Euler path.

2. A graph has an Euler circuit if and only if the degree of every vertex is even. A graph has an Euler path if and only if there are at most two vertices with odd degree.

Step-by-step explanation:

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3 years ago

a cardboard box holds 31.25 cubic inches of creamy butter. The butter is molded into a square prism that is 5 inches long. How m

lesya [120]

Answer:

$62.5 \:in^2$

Step-by-step explanation:

Volume of the butter in the cardboard = 31.25 cubic inches

Length of the Molded Square Prism =5 Inches

Let the length of the square cross sectional area = x

Volume of the Prism $=x^2l$

Since l=5 Inches

$5x^2=31.25\\x^2=6.25\\x=2.5\: Inches$

Next, we determine the surface area of the New Cardboard box to be made.

Length of the Cardboard Box=5 Inches

Length of the square cross sectional area = 2.5 Inches

Total Surface Area $=2(x^2+xl+xl)=2(x^2+2xl)$

$=2(2.5^2+2(2.5)(5))\\=2(6.25+25)\\=2*31.25\\=62.5 \:in^2$

Therefore, $62.5 \:in^2$ of cardboard is needed,

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3 years ago

The average height of 20-year-old American women is normally distributed with a mean of 64 inches and standard deviation of 4 in

Murrr4er [49]

Answer:

Probability that average height would be shorter than 63 inches = 0.30854 .

Step-by-step explanation:

We are given that the average height of 20-year-old American women is normally distributed with a mean of 64 inches and standard deviation of 4 inches.

Also, a random sample of 4 women from this population is taken and their average height is computed.

Let X bar = Average height

The z score probability distribution for average height is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 64 inches

$\sigma$ = standard deviation = 4 inches

n = sample of women = 4

So, Probability that average height would be shorter than 63 inches is given by = P(X bar < 63 inches)

P(X bar < 63) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{63-64}{\frac{4}{\sqrt{4} } }$ ) = P(Z < -0.5) = 1 - P(Z <= 0.5)

= 1 - 0.69146 = 0.30854

Hence, it is 30.85% likely that average height would be shorter than 63 inches.

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3 years ago