Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

  1. Bicycle wheel
    cyklo2_2 After driving 157 m bicycle wheel rotates 100 times. What is the radius of the wheel in cm?
  2. Rectangle 39
    rectnagles Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
  3. The cellar
    X Mr Novák has a cellar and a cellar window in the chalet has 0.6 meter square window. The window wishes to place an X-shaped grid in a square. He uses iron welded bars. Calculate the lengths of individual bars and what the total length of the bars he has t
  4. The terrace
    terasa Around the round pool with a diameter of 5.5 meters is a wooden terrace with a width of 130 cm. What is the area of the terrace?
  5. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  6. Broken tree
    stromy_4 The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
  7. Trapezium
    trapezium_1 The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
  8. Circle chord
    circles_6 Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
  9. The rope
    rhombus-diagonals_2 A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners?
  10. Parabola 3
    parabola_2 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
  11. Folded square
    square_folded ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
  12. MO Z8–I–6 2018
    lich_1 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
  13. Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  14. ABCD
    trig_1 AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
  15. 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.
  16. Circle area
    circle3 Calculate the circle area with a radius of 1.2 m.
  17. Diagonals
    rhombus_3 A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
  18. Diagonal
    trapezium_right_1 he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
  19. Trapezium internal angles
    lichob_2_2 A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
  20. Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.

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