Diagonal - 8th grade (13y) - examples

  1. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  2. Rectangle diagonal
    rectnagles_3 The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
  3. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  4. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
  5. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  6. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
  7. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
  8. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  9. Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
  10. 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.
  11. Rhombus
    rhomus_circle It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  12. Rectangle
    golden-rectangle-ratio Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
  13. Rhombus and inscribed circle
    rhombus_2 It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals.
  14. Rectangle
    rectangle_ABCD In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
  15. Rhombus
    rhombus_1 Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
  16. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  17. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  18. Prism
    prism_rhombus_1 Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
  19. Square 2
    square_ABCD_1 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
  20. Square
    1square Calculate area of the square with diagonal 64 cm.

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.



To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.