Diagonal + Pythagorean theorem - math problems

  1. Diamond area from diagonals
    kosostvorec In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
  2. Height of pyramid
    ihlan The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
  3. Wall and body diagonals
    cube_diagonals The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
  4. Height of the cuboid
    diagonal_rectangular_prism Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
  5. Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  6. Three faces of a cuboid
    cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
  7. Two circles
    intersect_circles Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
  8. Inscribed circle
    Cube_with_inscribed_sphere A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
  9. A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  10. The trapezium
    rt_iso_triangle The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
  11. Cuboid face diagonals
    face_diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
  12. Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  13. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
  14. Wall and body diagonals
    diagonals_prism Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
  15. Company logo
    circle_square_insribed The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
  16. Area of a rectangle
    rectangle Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
  17. Right pyramid
    squarepyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
  18. Tree trunk
    circle_and_square What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
  19. Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
  20. Ratio of sides
    described_circle2 Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.

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Pythagorean theorem is the base for the right triangle calculator.