Pythagorean theorem + expression of a variable from formula - problems

  1. Three altitudes
    triangle_vysky A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
  2. Right Δ
    ruler A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  3. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 9921 cm3. Determine the length of the edges of a cube.
  4. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  5. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  6. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  7. 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.
  8. Right triangle
    righttriangle Legs of right are in ratio a:b = 2:8. Hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  9. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
  10. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  11. ISO triangle
    rr Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
  12. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  13. Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  14. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  15. Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  16. Perimeter and legs
    RT_triangle Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
  17. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  18. Trapezoid
    lichobeznik_3 trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
  19. Rectangle diagonals
    rectangle_diagonals_1 It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
  20. Nice prism
    diagonal_rectangular_prism.JPG Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.

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Pythagorean theorem is the base for the right triangle calculator.