7th grade (12y) + Pythagorean theorem - examples

  1. 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?
  2. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  3. Square
    square_1 Points A[-10,-1] and B[2,-1] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  4. Is right?
    rtriangle Is triangle with sides 51, 56 and 77 right triangle?
  5. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 33 km.
  6. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
  7. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
  8. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
  9. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  10. Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  11. Right triangle
    righttriangle Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
  12. Ladder
    rebrik_1 Ladder 8 m long is leaning against the wall. It foot is 1 m away from the wall. In which height ladder touch the wall?
  13. Triangle
    eq_triangle Can be rectangular triangle equilateral?
  14. Octagon
    8gon We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
  15. Cap
    cone_hat Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
  16. Rhombus
    rhombus_1 Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
  17. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  18. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
  19. Road embankment
    nasyp_cesta Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
  20. Canopy
    cone-roof Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?

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Pythagorean theorem is the base for the right triangle calculator.