Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid:
sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm
angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.)
S =? , V =?

Correct result:

h =  10.3923 cm
S =  936 cm2
V =  1621.2 cm3

Solution:

a1=18 cm a2=6 cm A=60   S1=a12=182=324 cm2 S2=a22=62=36 cm2 t=tanA=tan60 =1.732051=1.73205 b1=a1/2=18/2=9 cm b2=a2/2=6/2=3 cm  h1=b1 t=9 1.7321=9 3 cm15.5885 cm h2=b2 t=3 1.7321=3 3 cm5.1962 cm  h3=h12+b12=15.58852+92=18 cm h4=h22+b22=5.19622+32=6 cm  h=h1h2=15.58855.1962=6 3=10.3923 cm
S3=a1 h3/2=18 18/2=162 cm2 S4=a2 h4/2=6 6/2=18 cm2 S=4 (S3S4)+S1+S2=4 (16218)+324+36=936 cm2
V=h/3 (S1+S1 S2+S2)=10.3923/3 (324+324 36+36)=1621.2 cm3



We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Tetrahedral pyramid
    jehlan_4b_obdelnik_3 Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
  • Regular triangular pyramid
    3sidespyramid_1 Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
  • Quadrilateral pyramid
    jehlan_2 A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
  • Quadrilateral pyramid
    jehlan_1 We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
  • Pyramid four sides
    jehlan_4b_obdelnik_1 In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
  • Triangular pyramid
    jehlan3_1 Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.
  • Find the
    ihlan Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm3 and a height of 45 cm.
  • Pyramid height
    pyramid333 Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • Isosceles triangle
    rr_triangle3_1 Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
  • Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  • Right angle
    triangles_1 If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • 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)?
  • 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?
  • 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?