9th grade (14y) + Pythagorean theorem - examples

  1. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  2. The perimeter
    hexagon6 The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
  3. Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
  4. A square
    rhombus3_3 A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
  5. Find the 3
    segment_2 Find the distance and mid-point between A(1,2) and B(5,5).
  6. Garden
    garden_1 Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
  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. 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.
  9. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
  10. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  11. 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?
  12. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  13. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  14. Cuboid
    cuboid Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm3. Calculate the length of the other edges.
  15. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
  16. 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°.
  17. Square
    square_1 Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  18. 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 26 km/h. Determine the distance between them after 35 minutes cycling.
  19. 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
  20. 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?

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Pythagorean theorem is the base for the right triangle calculator.