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

Pythagorean theorem is the base for the right triangle calculator.

  1. Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
  2. Tangent 3
    tangetns In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
  3. Chord
    tetiva2_1 It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
  4. Surface area of the top
    cylinder_4 A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
  5. The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  6. Garden
    garden_1 Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
  7. Right Δ
    ruler Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  8. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
  9. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
  10. Circle chord
    circleChord What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm?
  11. Rectangle
    rectangle_inscribed_circle The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
  12. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°.
  13. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
  14. Is right?
    rtriangle Is triangle with sides 24, 51 and 45 right triangle?
  15. Square
    square_1 Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  16. Movement
    peleton From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling.
  17. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  18. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 55 dm.
  19. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 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?
  20. River
    river From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river.

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