9th grade (14y) + Pythagorean theorem - math problems

  1. The tractor
    tractor The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m?
  2. 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.
  3. 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.
  4. 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?
  5. Base of prism
    hranol3b The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
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  7. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  8. 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?
  9. Right Δ
    ruler A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  10. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 3234 cm3. Determine the length of the edges of a cube.
  11. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
  12. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if the distance from the center circle is 16 m?
  13. Rectangle
    rectangle_inscribed_circle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
  14. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  15. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  16. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
  17. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  18. Movement
    peleton From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
  19. Square
    square_1 Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
  20. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.

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Pythagorean theorem is the base for the right triangle calculator.