# Problems of area of plane shapes - page 7

1. Rectangle A2dim Calculate the side of the rectangle, if you know that its area is of 2590 m2 and one side is 74 m.
2. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
3. Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
4. Triangular prism Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
5. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
6. Axial section Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
7. Circles Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
8. Isosceles III The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
9. Rectangle Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
10. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
11. Children pool The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film.
12. Garden 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.
13. Tetrahedral prism Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
15. Similarity n-gon 9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
16. Rhombus HP Calculate area of the rhombus with height 24 dm and perimeter 12 dm.
17. Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
18. Tiles From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
19. ISO trapezium Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
20. Truncated pyramid How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm?

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