Hexagonal pyramid

Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.

Result

h =  19.526 cm

Solution:

a=5 cm w=20 cm r=a=5=5 cm  s2=(a/2)2+w2 s=(a/2)2+w2=(5/2)2+20220.1556 cm  s2=r2+h2  h=s2r2=20.155625219.5256=19.526  cm a = 5 \ cm \ \\ w = 20 \ cm \ \\ r = a = 5 = 5 \ cm \ \\ \ \\ s^2 = (a/2)^2 + w^2 \ \\ s = \sqrt{ (a/2)^2 + w^2 } = \sqrt{ (5/2)^2 + 20^2 } \doteq 20.1556 \ cm \ \\ \ \\ s^2 = r^2 + h^2 \ \\ \ \\ h = \sqrt{ s^2-r^2 } = \sqrt{ 20.1556^2-5^2 } \doteq 19.5256 = 19.526 \ \text{ cm }



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Regular hexagonal pyramid
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
  2. Tetrahedral pyramid
    jehlan_3 It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
  3. 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
  4. Tetrahedron
    3sidespyramid What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
  5. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  6. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  7. Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  8. Median
    medians.JPG In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
  9. Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  10. Isosceles trapezoid
    lichobeznik_mo_z8_5 What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
  11. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  12. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  13. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  14. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  15. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  16. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  17. The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?