Examples of area of plane shapes - page 23

  1. The perimeter
    hexagon6 The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
  2. Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
  3. Equilateral triangle
    equilateral_triangle2_1 Calculate the area of an equilateral triangle with circumference 72cm.
  4. Sand path
    sand_1 How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
  5. Two rectangles
    rectangles2_2 I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
  6. Coordinate axes
    tr_triangle_axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
  7. Diameter to area
    circle_eq_1 Find the area of a circle whose diameter is 26cm.
  8. The room
    malovka_5 The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
  9. Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
  10. Square prism
    lichob_2 Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
  11. Base of house
    domcek_4 Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m.
  12. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  13. Garden
    garden_18 The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?
  14. Triangular prism
    prism_4 Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters.
  15. Area of garden
    garden_20 If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
  16. Annual rainfall
    rain_7 The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
  17. The sides 2
    trapezium_7 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
  18. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  19. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  20. Ratio of sides 2
    square_5 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.

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