Examples of area of plane shapes

  1. Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  2. Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  3. Circles
    two_circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
  4. Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.
  5. Triangle
    triangle_circle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
  6. Rail turn
    railroad_turn The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve.
  7. Tinsmith
    rury Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate?
  8. Wiring
    install_pipes Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 $mm2?
  9. Wheat
    field_1 The rectangle shaped field with dimensions 1268 m and 745 m harvested last year was 4959 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 4 m parallel to the side of the field 745 m, where
  10. Expansion
    magnification If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
  11. Garden
    lichobeznik_zachradka The garden has two opposite parallel fences. Their distance is 33.1 m. Lengths in these two fences are 75.5 meters and 49.4 meters. Calculate the area of this garden.
  12. Floor
    map_mierka The floor area of ​​the room is 31 m2 and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75?
  13. Rectangle
    diagonal In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  14. Wire
    cu_wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
  15. Cable
    wire Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
  16. Square
    1square Calculate area of the square with diagonal 64 cm.
  17. Pipeline
    pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
  18. Circles 2
    zlozite_kruznice Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
  19. Arc and segment
    odsek_kruh Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
  20. Rectangular field
    field One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...