How many sides does this polygon have ?

Mathematics

2 answers:

maks197457 [2]3 years ago

8 0

Answer:

Step-by-step explanation:

To get the measure of the interior angle of a polygon we use the formula (n-2)×180÷n where n is the number of sides of the polygon

We can use this formula in this question by sitting an equation and solving for n

(n-2)×180÷n = 172

Multiply both sides by n

(n-2)×180 = 172n

Distributing the 180

180n - 360 = 172n

Adding 360 and subtracting 172n from both sides

8n = 360

Dividing both sides by 8

N = 45

Zielflug [23.3K]3 years ago

4 0

A polygon has 3 sides

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Find the island height of a pyramid with a volume of 432 ft^3 if the base is a square with a side length of 12 ft. Round to the

dmitriy555 [2]

So the picture below shows what the slant height is. It also shows that the pyramid can form a right triangle, in which we can use the pythagorean theorem, which is $leg^2+leg^2=hypotenuse^2$ .

But first, we have to find the height of this pyramid. The volume formula for a square pyramid is $A=\frac{lwh}{3}$ . Since we know its a square pyramid, the length and width are going to be the same (12 ft), and we know that the volume is 432 ft^3. Using this info, we can solve for the height:

$432=\frac{12*12*h}{3}\\ 1296=12*12*h\\ 1296=144*h\\ 9=h$

So now we can use the pythagorean theorem (remember to split the 12 by 2, since the right triangle has only half the length of the base). Our equation will be solved as such:

$6^2+9^2=s^2\\ 36+81=s^2\\ 117=s^2\\ 10.8=s$