Geometry

posted by .

Find the area of a regular pentagon with radius 3cm. Round to the nearest tenth.

No picture is given, but I believe a circle can surround the figure. I'm not really sure how to find the area of the figure when the side length isn't given. Can you guys help me?

Thanks much!

  • Geometry -

    if it fits inside the circle, the distance from the center to a point of the pentagon is 3 cm.
    There are five isoceles triangles in the pentagon, each with an angle at the center of 360/5 = 72 degrees and sides of 3 cm
    What we have to do is find the area of that triangle and multiply by 5
    we need the base of the triangle and its altitude
    look at right triangle formed by altitude and base
    72/2 = 36 degrees
    hypotenuse = 3
    so altitude /3 = cos 36
    half base/3 = sin 36
    altitude = 2.43
    half base = 1.76
    area of isoceles triangle = half base * altitude = 4.28
    5 times triangle area = 21.4
    ===============================
    rough check (credit Archimedes)
    area of circle around it = pi (3)^2 = 28.3 so or answer is not crazy

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geometry

    Find the area of a circle circumscribed about a regular hexagon with an apothem of 5 inches. Round to the nearest tenth
  2. Geometry

    Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle?
  3. Geometry - Bob

    Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle?
  4. geometry

    Find the area of a regular pentagon with a side of 6ft. answer nearest tenth
  5. Math.

    1. Find the area of the given circle. Round to the nearest tenth. *theres a picture of a circle and the radius is 3.5* A. 22.0 cm *squared* B.38.5 cm *squared* C. 11.0 cm *squared* D. 42.8 cm *squared* 2.Find the circumference of the …
  6. geometry

    find the area bounded by a regular pentagon with radius 6 cm. round to the nearest tenth.
  7. Math

    19. WorkPad Note: In questions 19-21, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?
  8. Math "Need Help Asap"!

    19. WorkPad Note: In questions 19-21, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?
  9. Geometry

    Regular pentagons A and B are similar. The apothem of Pentagon A equals the radius of Pentagon B. Compare the areas. The area of Pentagon A is equal to 1.49 times the area of Pentagon B. The area of Pentagon B is equal to 1.49 times …
  10. Math

    I help solving these out can someone work through them with me?

More Similar Questions