Examples of area of plane shapes

Area of ditch
How great content area will have a section of trapezoidal ditch with a width of 1.6 meters above and below 0.57 meters? The depth of the ditch is 2.08 meters.
Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
Square garden
On the plan with a scale of 1:1500 is drawn as a square garden with area 81 cm². How many meters is long garden fence? Determine the actual acreage gardens.
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.
Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
Trapezium
The area of trapezium is 35cm² find its altitude if the bases are 6cm and 8cm.
Regular quadrangular pyramid
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca
Square plate
From a square metal plate with a side long 6dm were cut two identical rectangular openings with dimensions of 2.5 dm and 2 dm. Calculate the remainder of the square plate.
Rotary cylinder
The rotating cylinder has a surface area 69.08 cm². The area of the shell is 62.8 cm ². What is the diameter of the cylinder?
Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
Trapezoid - hard example
Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
Percentage of waste
In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste.
Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (surface area)?
Plumber
Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
Goat
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?
Triangle
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.

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