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wariber [46]
3 years ago
7

In the regular octagon, the numeric value of the area of the shaded region is twice more than the numeric value of the length of

AB. Find the area of the unshaded region.
Mathematics
1 answer:
s2008m [1.1K]3 years ago
8 0

Answer:

A =  (2+√8)L² - 2L, where L is the length of AB

Step-by-step explanation:

Lets call L the length of one side. The octagon can be divided in 8 triangles composed by the vertices of the octagon and the center. The base of each triangle has length L and the height is L/2 + M, with M such that 2M² = L². This is because the center of the octagon is located at middle height of the center sides. You can reach that height by 'travelling' from the bottom side throught one slanted side (which is the hypotenuse of a isosceles rectangle triangle of height M) and then you travel throught a center side half its length. Thus, h = L/2 + L/√2.

The area of each triangle of the octagon therefore is, as a result, h*L/2 = L²/4 + L²/2√2

Hence, the area of the octagon is 8*(L²/4 + L²/2√2) = (2+√8)L². The unshaded region area can be computed by taking this number and substract to it the value of 2L, which is the area of the shaded region (The double of the length of a side)

As a result,

A =  (2+√8)L² - 2L

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The Earth has a mass of about 6 x 10^24 kg. Neptune has a mass of 1.8 x 10^27kg. How many times bigger is Neptune than Earth
elena-s [515]

Answer:

300 times bigger.

Step-by-step explanation:

That would be (1.8 * 10^27 ) / (6 * 10^24)

= 0.3 * (10^27/10^24)

= 0.3 * 10^3

= 3 * 10^2

= 300.

5 0
3 years ago
1+3x=x+9 solve for x.. Help?
anzhelika [568]

Answer: <em>x=4</em>

Step-by-step explanation:

<em>1+3x=x+9</em>

<em>   -x  -x</em>

<em>1+2x=9</em>

<em>-1      -1</em>

<em>2x=8</em>

<em>Divide by 2 on each side</em>

<em>Final result</em>

<em>x=4</em>

7 0
3 years ago
You read 16 pages in 20 minutes and your friends read 25 pages in 30 minutes who reads faster​
guapka [62]

Answer:

You read faster because in 20 minutes you read 16 pages but your friends had 30 minutes they had more time that's why they read more pages not because they read fast

6 0
3 years ago
Read 2 more answers
Find the area of the shaped region
Ganezh [65]

Answer: B

Step-by-step explanation:

A = 0/360 ×π×r^2

=135/360×π×11×11

=142.55 yd^2

5 0
3 years ago
How to solve this problem​
nevsk [136]

Let C be the center of the circle. The measure of arc VSU is 2+114x, so the measure of the minor arc VU is 360-(2+114x)=358-114x. The central angle VCU also has measure 358-114x.

Triangle CUV is isosceles, so the angles CVU and CUV are congruent. The interior angles of any triangle are supplementary (they add to 180 degrees) so

m\angle VCU+2m\angle CUV=180

\implies m\angle CUV=\dfrac{180-(358-114x)}2=57x-89

UT is tangent to the circle, so CU is perpendicular to UT. Angles CUV and VUT are complementary, so

(57x-89)+(31x+3)=90

\implies88x=176

\implies x=2

So finally,

m\widehat{VSU}=2+114\cdot2=230

degrees.

6 0
3 years ago
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