posted by .

area of a nonagon with a perimeter of 126in

  • math -

    The area A of any regular polygon of n sides with side length s, apothem a is
    Since ns=perimeter, p, we can also write the area as

    An apothem is the distance from the centre of the polygon to the side.

    We assume the given nonagon is regular, i.e. all sides and interior angles are equal.

    A nonagon has 9 sides. Each side is of length 126/9=14". We need first to find the apothem as follows.

    The central angle for each side is 360/9=40°.

    Each side of the nonagon forms an isosceles triangle with the centre of the nonagon. Its half vertical angle equals 40/2=20°.

    The height of this triangle is the apothem and can be calculated by the trigonometric formula

    Using the formula above:
    Area = ap/2=126*7cot(20)=882cot(20°)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 2nd grade math

    If you have a rectangle with 24 square units 3 lines down 8 across how can you have a 4 unit rectangle with a perimeter of 8 around the outside also 6 units with a perimeter of 10 in a seprate problem A square of 4, perimeter of 8. …
  2. math

    one of the two numbers that can be both the perimeter and the area of the same rectangle I am assuming that you are seeking the two rectangles that have the area equal to the perimeter. A 4 x 4 square has a perimeter and area of 16. …
  3. Geometry

    Find the area of a nonagon with a perimeter of 126 inches. Round to the nearest tenth.
  4. Math

    There's a triangle the numbers on each sides are 22 25 and 11 What is it's perimeter and area?
  5. Math

    find the sum of the interior angles of a nonagon. I know a nonagon has 9 sides.. A. 140 degrees B. 1,620 degrees C. 1,260 degrees D. 1,450 degrees If the question is asking for each interior angle then I think the answers A but if …
  6. Math-7th grade

    A scale drawing is a parallelogram with a base of 8 inches, a height of 3 inches, and a side length of 4 inches. What is the perimeter and area?
  7. Math

    Find the perimeter and the area of the rectangle. I cant upload pics. Its a rectangle with 12cm at the bottom and theres a diaganal line going through and its 15cm Perimeter: 54 cm, Area: 180 cm^2 Perimeter: 54 cm, Area: 108 cm^2 Perimeter: …
  8. 6 grade math area perimeter

    I found the area but I need help on perimeter. The shape in form of letter L. The long is a 1×4 and the box on top is a 1×1. THE AREA IS 5 sq.units I think perimeter is 12 is this right
  9. 6 grade math area perimeter

    I want to make sure this one is ok. I know the area now I need perimeter. It's a long line it's a 1× 6 and on top in the middle is another box 1×2 shape the area I got was 8 sq.units. I think perimeter is 15units. Is this right
  10. Math

    if you fold a square paper vertically, the new rectangle has a perimeter of 39cm. what is the area of the original square?

More Similar Questions