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3 years ago

Find the area. Photo Attached

Mathematics

1 answer:

Delvig [45]3 years ago

7 0

Answer:

Area of Regular Polygon: ( About ) 716.6 m^2; Option B

Step-by-step explanation:

~ In this situation we can apply the formula 1/2 * a * P, provided a ⇒ apothem, and P ⇒ Perimeter of the shape ~

Here we are not directly provided with the apothem, so we have to first plan out our procedure step-by-step:

Let us first divide this dodecagon into 12 triangles, each equilateral provided that this is a regular polygon ( implied ). Now let us draw an altitude to one of these triangles, and provided these are equilateral triangles Coincidence Theorem can be applied to this specific triangle. That would mean this altitude is both an angle bisector and a median, which can help us determine the tan degree of the mini triangle formed by the altitude, and the length of one of the sides of this mini triangle.

1. Knowing that the altitude splits the base of the triangle into the two congruent parts ⇒ one of the congruent parts should be ⇒ 8/2 = 4 meters

2. Now the triangles formed through spliting this figure are all ≅, so one of the angles of the triangle is 360/12 = 30 degrees. The mini triangle formed should thus have a measure of 30/2 as the altitude is an angle bisector ⇒ tan 15.

3. From this you can create a proportion, with a ⇒ apothem:

tan 15/ 1 = 4/a ⇒ tan 15 * a = 4 ⇒ a = 4/tan 15° ⇒ a = ( About ) 14.93

4. The perimeter of this shape would be 8 * 12 ⇒ 96 meters

5. Now let us solve for the area of this regular polygon through substitution into the formula 1/2 * a * P ⇒ 1/2 * 14/93 * 96 = ( About ) 716.64 meters^2

Answer ⇒ Area of Regular Polygon: ( About ) 716.6 m^2

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the intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hour

Leona [35]

The outlet pipe will take 18 hours to empty the tank.

Step-by-step explanation:

Number of hours taken by inlet pipe to fill the tank=6

work done by the inlet pipe in 1 hour=1/6

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work done by the inlet pipe in 1 hour with outlet pipe open=1/9

we have to determine the time taken by the outlet pipe to empty the tank

The inlet and outlet pipe does the opposite work.

$\\time\ taken\ by\ the\ outlet\ pipe\ to\ empty\ the\ tank=x\\work\ done\ by\ the\ outlet\ pipe\ in\ 1\ hour=1/x\\(1/6-1/x)9=1\\1/6-1/x=1/9\\1/x=1/6-1/9=3/54\\x=54/3=18$

The outlet pipe takes 18 hours to empty the tank.

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3 years ago

Calculate the area of the following figure correct to 2 decimal places if can show or explain work

grin007 [14]

The way we approach a question like this, is by looking at what portion of the circle we actually have to calculate the area of. We know that a circle is a shape that goes 360 degrees around a point. Therefore we know that, for example, a semicircle, or half a circle, would cover half the amount of degrees. This is important, because as well as covering half the number of degrees, it also covers half the area. For the figure in your picture, we are told that the portion missing from the circle is 90 degrees (shown by the right angle symbol in the center).
this means that 90 degrees worth of the circle is missing, so if we do 360÷90, we find that the answer equals $\frac{3}{4}$ . This means that we are dealing with $\frac{3}{4}$ of a circle. So, we simply find the area of the circle normally, and then multiply by $\frac{3}{4}$ :
The formula for area of a circle is $\pi r^{2}$ , so in this case, it can be said to be $\pi (10^{2} )$ , which is equal to 314.15
Now we simply take that area and multiply it by the fraction we established earlier:
314.15 x $\frac{3}{4}$ = 235.61
Therefore the area of the figure is 235.61 $cm^{2}$
I hope this helped and please remember to try and not only understand the answer, but the maths that worked it out too :))

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4 years ago