What is the area of a 15-gon with a perimeter of 90 m

Area of the polygon = 635.13 m²

Step-by-step explanation:

Since area of the polygon = (1/2) × perimeter × apothem

We have to calculate the are of a 15-gon with a perimeter 90 m.

Here parameter is given and we have to calculate the value of apothem.

Since side of a polygon = perimeter / total number of sides = 90/15 = 6

Now if we take an example of pentagon as shown in the figure, number of triangles formed at the center A is equal to number of sides of a polygon.

And in a triangle formed by ABC in any polygon ∠BAC = 360°/ (n) number of sides.

Now we come back to our question ∠BAC = 360/15 = 24

and ∠BAD = 12°(AD is the perpendicular bisector of BC)

Now tan 12 = 3/ h

⇒ 0.2125 = 3/ h

⇒ h = 3/0.2125 = 14.114 m

Now we apply the formula to calculate the area of the polygon.

Area = (1/2) × perimeter × apothem (h)

=(1/2)×90×14.114 = 635.13 m²

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2