Diagonal - examples

  1. Diagonals of a rhombus
    rhombus-diagonals_1 One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
  2. Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  3. Rhombus and diagonals
    kosostvorec_2 The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
  4. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  5. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  6. KLMN
    trapezium In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
  7. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  8. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  9. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  10. N-gon
    ngon How many diagonals has convex 29-gon?
  11. See harmonics
    HarmonicMean It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
  12. Diagonal
    diamond Can be a diagonal of diamond twice longer than it side?
  13. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 15 cm and 27 cm long.
  14. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  15. Prism
    prism-square The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
  16. Trapezoid MO-5-Z8
    lichobeznik_mo_z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
  17. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.
  18. Diagonal in rectangle
    q In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
  19. Square
    1square Calculate area of the square with diagonal 70 cm.
  20. Rectangle
    rectangle_ABCD In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.

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