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3 years ago

The base of a regular pyramid is a hexagon.

Mathematics

2 answers:

Leona [35]3 years ago

8 0

ANSWER

$96 \sqrt{3} {cm}^{2}$

EXPLANATION

The area of a regular polygon is

$Area= \frac{1}{2} ap$

where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.

From the diagram,

$\sin(60) = \frac{a}{8}$

a=8sin(60)

$a = 4 \sqrt{3}$

$\cos(60) = \frac{l}{8}$

$l = 8 \cos(60)$

$l = 4$

The length of one side of the hexagon is 2×4=8.

The perimeter of the hexagon is

p=6×8=48

The area of the hexagon is

$= \frac{1}{2} \times 4 \sqrt{3} \times 48$

$= 96 \sqrt{3} {cm}^{2}$

VladimirAG [237]3 years ago

4 0

Answer:

the correct answer is 96√3 i just took the unit test. have a blessed day :)

Step-by-step explanation:

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35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Find the area of the larger circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

7 0

3 years ago

Evaluate the piecewise function for the given values.

adoni [48]

Answer:

f(-3) = -2

f(-2.6) = -2

f(0.6) = 2.4

f(4.5) = 8.5

Step-by-step explanation:

(Whole question:

Evaluate the piecewise function for the given values.

Find f(-3), f(-2,6), f(0.6), and f(4.5) for f(x)={ -2 If x ≤ 0 4x. If 0 <x <1. x + 4. If x ≥ 1)

As the piecewise function shows, the function f(x) has the value of -2 for values of x lesser or equal than 0, has the value of 4x if the value of x is between 0 and 1, and has the value of x+4 for values of x greater or equal than 1.

So, for f(-3), the value of x is lesser than 0, so we have that f(-3) = -2

For f(-2.6), the value of x is lesser than 0, so we have that f(-3) = -2

For f(0.6), the value of x is between 0 and 1, so we have that f(0.6) = 4*0.6 = 2.4

For f(4.5), the value of x is greater than 1, so we have that f(4.5) = 4.5 + 4 = 8.5

5 0

3 years ago

BRAINLIEST GIVEN TO BEST ANSWER

lbvjy [14]

Answer:

Slope = $\frac{1}{4}$

Step-by-step explanation:

Slope of a straight line passing two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula,

m = $\frac{y_2-y_1}{x_2-x_1}$

From the graph attached,

Line is passing through two points (20, 5) and (80, 20),

Therefore, slope of the line will be,

m = $\frac{20-5}{80-20}$

m = $\frac{1}{4}$

The slope is $\frac{1}{4}$ .

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3 years ago

(5y 3 + 20y 2 – 12)(2y3 - 15y2 + 4y + 16)

Alex

Answer:

225y5-192

Step-by-step explanation:

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3 years ago

There are 100 balloons in total the ratio between the yellow and blue balloons is 8 to 12 how many are yellow

Virty [35]

If you have 8 yellow balloons for every 12 blue balloons, then if you have 20 balloons in total, 8 out of 20 of those balloons will be yellow. Then you can set up this ratio.

Then, you can use either cross multiplication or multiply the numerator and denominator by the same number to help solve for x. Personally, I prefer cross multiplication.

Finally, solve for x and if you had 100 balloons, you will have 40 yellow balloons.

4 0

3 years ago

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