Examples of area of plane shapes

  1. Tiles
    kachlicky Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
  2. Pit
    truncated_pyramid Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when
  3. Glass
    glass Peter broke the window glass with size 110 cm and 90 cm. 1 square meter of glass costs 11 USD. How much money is need to pay for a new glass?
  4. Hřiště
    playground Map scale is 1: 5000. The playground is rectangular and on the map has dimensions 10 cm and 5 cm What is area of playground in square meters in reality?
  5. Triangular prism
    TriangularPrism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
  6. Playground
    plot_ihrisko.JPG Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
  7. Mystery of stereometrie
    Tetrahedron Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
  8. Diagonals in the diamond
    kosoctverec_color The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
  9. Quadrilateral
    diamond_2 In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
  10. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  11. Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  12. Park
    park_voda In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
  13. RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  14. Rectangle - sides 3
    stvorec If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we inc
  15. Tiles
    dlazdice From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
  16. Triangle
    triangle_ABC_1 The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
  17. Diamond
    diamond_1 Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
  18. Box
    Rhombic_prism Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of a
  19. Leg
    tetris Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
  20. Inscribed rectangle
    circle_desc_rectangular The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.

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...