8th grade (13y) + Pythagorean theorem - examples

  1. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20m west, 30m north and 10m west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  2. Cone 15
    cone_9 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
  3. Garden
    garden_1 Area of 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?
  4. Right Δ
    ruler Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
  5. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 3724 cm3. Determine the length of the edges of a cube.
  6. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  7. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  8. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  9. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
  10. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
  11. Movement
    peleton From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 16 km/h. Determine the distance between them after 35 minutes cycling.
  12. Square
    square_1 Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  13. Is right?
    rtriangle Is triangle with sides 51, 56 and 77 right triangle?
  14. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  15. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  16. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
  17. 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 254 cm2.
  18. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
  19. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 33 km.
  20. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.

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Pythagorean theorem is the base for the right triangle calculator.