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zysi [14]
3 years ago
9

find the area of the regular decagon if the apothem is 5 inches and a side is 3.2 inches. Round to the nearest whole number

Mathematics
1 answer:
Lilit [14]3 years ago
3 0

When you are given the side length and apothem of a regular polygon and asked for area, you are expected to use the formula

... A = (1/2)Pa

where P is the perimeter of the polygon, "a" is the apothem, and A is the area.

The only additional information you need is that a decagon has 10 sides, so its perimeter is 10×3.2 inches = 32 inches.

The area is ...

... A = (1/2)(32 in)(5 in)

... A = 80 in²

_____

Sometimes the dimensions of a problem like this don't quite add up. The geometry of a regular polygon means that the apothem can be found from the side length and vice versa. In this case, the side length of 3.2 inches means the apothem is about 4.92 inches; or the apothem of 5 inches means the side length is about 3.25 inches. Either way, the area is slightly different from that computed using the given numbers.

This is why I say you're expected to use the above formula. (You're not expected to think about it too much.)

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Diamonds have a density of 3.5 LaTeX: \frac{g}{cm^3}g c m 3. How big is a diamond that has a mass of 0.10 g?
liubo4ka [24]

For this case we have that by definition, the density is given by:

d = \frac {M} {V}

Where:

M: It is the mass of the diamond

V: It is the volume of the diamond

According to the data of the statement we have:

d = 3.5 \frac {g} {cm ^ 3}\\M = 0.10 \ g

So the volume is:

V = \frac {M} {d}\\V = \frac {0.10 \ g} {3.5 \frac {g} {cm ^ 3}}\\V = 0.02857\\V = 0.03 \ cm^3

Thus, the volume of the diamond is approximately 0.03 \ cm ^ 3

Answer:

0.03 \ cm ^ 3

3 0
3 years ago
Find the slope of the line through the given points.<br> (-2,6) and (2,-2)
Elenna [48]

Answer:

-2

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -2-6)/(2- -2)

   = ( -2-6)/( 2+2)

   -8/4

   -2

4 0
3 years ago
Read 2 more answers
Rachel mows 5 lawns in 8 hours. At this rate how many lawns can she mow in 40 hour?
posledela

We can think of this as an equality

5 Lawns = 8 Hours

If she needs 40 hours, you can multiply 8 hours by 5 to get 40, but now it's not balanced. So, you need to multiply 5 to the other side too so:

5 x (5) = 8 x (5)

Therefore she mows 25 Lawns in 40 Hours

5 0
3 years ago
A square mosaic is made of small glass squares. If there are 256 small squares in the mosaic how many are along an edge?
Degger [83]
To do this, you got to square 256.

The square root of 256 is 16.

Therefore, there are 16 small squares on each edge of the mosaic.

Kinda proof:

o  o  o  o  O
o  o  o  o  O
o  o  o  o  O
o  o  o  o  O
o  o  o  o  O

25 squares. Square root is 5. 5 along each edge. My work shares same concept.

Extremely unnecessary proof:

o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
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o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O
o   o   o   o   o   o   o   o   o   o   o   o   o   o   o   O

There are 256 squares, and you can count 16 on each edge. this shows 16 times 16, or 16 squared, which is 256.

3 0
3 years ago
Read 2 more answers
Twelve less than a number is 50.
Katen [24]

Answer:

62

Step-by-step explanation:

another way to write this is

x - 12 = 50

the answer is 62

62 - 12 = 50

7 0
3 years ago
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