Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?

Correct result:

S =  71.79 cm2

Solution:

a=5 cm h=8 cm V=28.8 cm3  h1=a2(a/2)2=52(5/2)24.3301 cm S1=a h12=5 4.3301210.8253 cm2    h22=h2+(h1/3)2 h2=h2+(h1/3)2=82+(4.3301/3)28.1292 cm  S2=a h22=5 8.1292220.3229 cm2  S=S1+3 S2=10.8253+3 20.322971.7941=71.79 cm2   Verifying Solution:  V2=13 S1 h=13 10.8253 828.8675 cm3 V2=V



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. 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:

  • 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?
  • Isosceles triangle
    rr_triangle3_1 Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
  • Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  • Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  • 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).
  • Isosceles trapezium
    rr_lichobeznik_2 Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
  • Right 24
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
  • 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.
  • 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.
  • Church roof
    veza_2 The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
  • Free space in the garden
    euklid The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
  • 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.
  • The bus stop
    jehlan_1 The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how many m2 roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage.
  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  • 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
  • Wall height
    jehlan_2 Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.