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. Chord circle
    Tetiva_1 The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
  2. Lawns
    grass Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?.
  3. Hypotenuse
    sqrt Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
  4. Circle - simple
    kruh The circumference of a circle is 930 mm. How long in mm is its diameter?
  5. Angles in ratio
    angles_1 The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
  6. Acreage
    pozemek Plot has a diamond shape, its side is 25.6 m long and the distance of the opposite sides is 22.2 meters. Calculate its acreage.
  7. Garden
    garden_7 The garden has a rectangular shape with lengths of 25 and 40 meters. It has been expanded so that each of its size increased by one fifth. How many square meters increased its acreage?
  8. 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?
  9. Forces
    vectors_4 Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
  10. Two circles
    two_circles Two circles with a radius 4 cm and 3 cm have a center distance 0.5cm. How many common points have these circles?
  11. Ace
    esicko The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
  12. 22/7 circle
    red_circle Calculate approximately area of a circle with radius 20 cm. When calculating π use 22/7.
  13. Kite
    drake_1 John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending.
  14. Midpoints
    rovnobeznik_4 Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
  15. Circle r,D
    bavlnka Calculate the diameter and radius of the circle if it has length 52.45 cm.
  16. Odometer
    s-l1000 The odometer is driven by rotation of the wheel whose diameter is 65 cm. After how many rotations the wheel turns counter to next kilometer?
  17. Circle's chords
    twochords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
  18. Diagonals of a rhombus
    rhombus-diagonals_1 One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
  19. Diamond perimeter
    Diamond_1000 Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm.
  20. Internal angles
    triangle_5 Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.

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