Square root + triangle - math problems

  1. Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  2. Garden
    garden_1 Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
  3. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
  4. Circle chord
    circleChord What is the length d of the chord circle of diameter 50 dm, if the distance from the center circle is 21 dm?
  5. Rectangle
    rectangle_inscribed_circle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
  6. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
  7. Is right?
    rtriangle Is triangle with sides 51, 56 and 77 right triangle?
  8. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  9. Square and circles
    kruznica_stvorec_1 Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  10. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
  11. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
  12. Area of RT
    right_triangle_sepia Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
  13. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  14. Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  15. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  16. Steps
    square_diagonal_1 How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
  17. Right triangle
    righttriangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  18. Isosceles right triangle
    3triangles Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
  19. Ladder
    rebrik_1 Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall?
  20. Tower
    HexagonalPyramid_4 The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?

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