Problems of area of plane shapes

  1. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  2. Map scale
    mapa_14 The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
  3. Coordinate axes
    tr_triangle_axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
  4. 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.
  5. Annual rainfall
    rain_7 The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
  6. Rectangle area
    rectangles_5 The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
  7. Pravoúhly trojúhelník
    tr_2 Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
  8. Garden
    garden_1 Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
  9. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  10. Right Δ
    ruler Right triangle has length of one leg 68 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
  11. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°.
  12. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
  13. Square
    square_1 Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  14. Scale
    pool_1 Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm2. What scale is the city plan?
  15. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 11 cm.
  16. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 26 cm and 42 cm long.
  17. Right triangle Alef
    r_triangle The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
  18. Tereza
    cube The cube has area of base 400 mm2. Calculate the edge length, volume and area of its surface.
  19. Rectangle
    diagonal In rectangle with sides 10 and 9 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?
  20. Area of RT
    right_triangle_sepia Calculate the area of a right triangle which hypotenuse has length 15 and one hypotenuse segment has lenght 11.

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