Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.

Correct result:

S =  273 cm2
V =  225.8 cm3

Solution:

h=6.5 cm A=42   tanA=h:(u/2) u=2 h/tanA=2 h/tan42 =2 6.5/tan42 =2 6.5/0.900404=14.43796  a=u/2=14.438/210.2092 cm  S1=a2=10.20922104.2274 cm2  h2=h2+(a/2)2=6.52+(10.2092/2)28.2648 cm  S2=a h2/2=10.2092 8.2648/242.1884 cm2  S=S1+4 S2=104.2274+4 42.1884=273 cm2
V=13 S1 h=13 104.2274 6.5=225.8 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 1 comment:
#
Peachpie1123
Thank u i was trying to find the answer to that in class(my teacher let us look it up and i said it so i got it right.

20 days ago  1 Like
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:

  • Quadrilateral pyramid
    jehlan_4b_obdelnik_1 The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
  • Quadrilateral pyramid
    jehlan_4b_obdelnik Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.
  • Digging a pit
    komoly_jehlan The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?
  • Triangular pyramid
    jehlan3_1 Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.
  • Five circles
    kruhy On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE
  • Acute triangle
    triangle2 In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles?
  • The staircase
    schody The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
  • There
    triangle_rt_taznice There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
  • Railway embankment
    rr_lichobeznik The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
  • Construction
    taznice7 Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction)
  • As shown
    rt_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE
  • Rhombus diagonals
    kosostvorec In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
  • A cliff
    cliff A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the​ cliff, how high is the​ cliff?
  • Isosceles triangle
    rr_triangle3_1 Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
  • Gardens
    garden The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
  • Given 2
    PQR_triangle Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find triangle area.
  • Calculate
    kuzel3 Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.