Examples of area of plane shapes - page 7
- 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.
- 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.
- Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
- 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
Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
- 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.
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.
- Quadrant II
Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
- 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.
- 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.
- Rhombus HP
Calculate area of the rhombus with height 24 dm and perimeter 12 dm.
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.
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
- 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.
- Concrete pipe
Concrete pipe is cylindrical with an inner diameter 110 cm and outer 120 cm. Calculate the surface of the concrete pipe, if it is 9 m long.
Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
- Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.