Examples of area of plane shapes

Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m² is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m² of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
RT 10
Area of right triangle is 84 cm² and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
Posters
Column with posters in the form of a cylinder is 2 m high and its diameter is 1.7 m. What is the content area for which it is possible to stick posters?
Rectangles - sides
One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm². What are the dimensions of the original rectangle?
Rectangle - sides
What is the perimeter of a rectangle with area 266 cm² if length of the shorter side is 5 cm shorter than the length of the longer side?
Roller
Roller has a diameter of 0.96 m and a width 169 cm. How many m² of road level when he turns 42-times?
7 triangle
The triangle area is 26.7 cm². Determine the side length l if appropriate height h_l = 45.3 cm.
Euklid4
Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
The pot
The pot is in 1/3 filled with water. Bottom of the pot has an area of 329 cm². How many centimeters rises water level in the pot after add 1.2 liters of water?
Rhombus
The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
Prism
Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle.
Right angled
From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
Areaf of ST
It is given square DBLK with side |BL|=13. Calculate area of triangle DKU if vertex U lie on line LB.
Garden
Rectangular garden has a length 99 m and width 84 m. Calculate how many m² will decrease its area if land by ornamental fence with width 30 cm.

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