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monitta
3 years ago
9

How do i find the perimeter of a regular polygon given the apothem

Mathematics
1 answer:
enyata [817]3 years ago
5 0
See attached picture:

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A circle has a square etched inside of it, with the endpoints of the square touching the circle. if the circle has a radius of 1
ch4aika [34]
First, illustrate the problem by drawing a square inside a circle as shown in the first picture. Connect each corner of the square to the center of the circle. Since the square is inscribed in the circle, they have the same center points. Each segment drawn to the corners is a radius of the circle measuring 1 unit. Also, a square has equal sides. So, the angle made between those segments are equal. You can determine each angle by dividing the whole revolution into 4. Thus, each point is 360°/4 = 90°.

Next, cut a portion of one triangle from the circle as shown in the second picture. Since one of the angles is 90°, this is a right triangle with s as the hypotenuse. Applying the pythagorean theorem,

s = √(1²+1²) = √2

So each side of the square is √2 units. The area of the square is, therefore,

A = s² = (√2)² = 2

The area of the square is 2 square units.

8 0
3 years ago
Circumference is 135.02 what is the diameter?
Ksju [112]

Answer:

86

Step-by-step explanation:

Radius=Circumference/Pi

135.02/3.14=43

Diameter=2r

43x2=86

5 0
3 years ago
I NEED HELP!!! What is is this ----&gt; 3x - 3y = 3 12x + 8y = -8 <br> x = what <br> y = what
fgiga [73]

Answer:

3x = 3 + 2y -------------> 3x - 2y = 3 {subtracted 2y from each side of top equation}

(-4/3)x + y = -2/3 ------> -4x + 3y = -2 {multiplied bottom equation by 3}

3x - 2y = 3 ------> 12x - 8y = 12 {multiplied top equation by 4}

-4x + 3y = -2-----> -12x + 9y = -6 {multiplied bottom equation by 3}

12x - 8y = 12

-12x + 9y = -6

--------------

y = 6 {added the two equations}

3x = 3 + 2y {original top equation}

3x = 3 + 2(6) {substituted 6, in for y, into top equation}

3x = 3 + 12 {multiplied}

3x = 15 {added}

x = 5 {divided each side by 3}

x = 5 and y = 6

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the midpoint of the segment with the following endpoints (4,5) and (1,2)
olga55 [171]

Answer:

Step-by-step explanation:

Mid point of two points is given as

Let Point 1 be(x1,y1)

And point 2 be (x2,y2)

Then, mid point is given as

M = [ (x1+x2) / 2 , (y1+y2) / 2 ]

So, given that,

Point 1 =(4,5)

Then, x1=4 and y1=5

Point 2=(1,2)

Also, x2=1 and y2=2

Then, applying the formulae

M = [ (x1+x2) / 2 , (y1+y2) / 2 ]

M = [ (4+1) / 2 , (2+5) / 2 ]

M = [ 5 / 2 , 7 / 2 ]

Then, the midpoint is

M=(5/2, 7/2)

To decimal point

M=(2.5 , 3.5)

To mixed fraction

M=(2½, 3½)

(x, y)=(2½, 3½)

5 0
3 years ago
The graph below shows Lisa's distance from her home (y), in miles, after a certain amount of time (x), in minutes:
steposvetlana [31]

Answer:

56

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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