Examples of area of plane shapes

Area is the quantity that expresses the extent of a two-dimensional shape. The area can be understood as the amount of paint necessary to cover the surface with a single coat. The area of a shape can be measured by comparing the shape to squares of a fixed size 1 m^2 or 1 cm^2 etc. Every unit of length has a corresponding unit of area. Areas can be measured in square metres (m^2), square centimetres (cm^2), square millimetres (mm^2), square kilometres (km^2), square feet (ft^2), square yards (yd^2), square miles (mi^2), and so forth.

Number of problems found: 702

Pipeline
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
Square
Calculate area of the square with diagonal 64 cm.
Arc and segment
Calculate the length of circular arc l, area of the circular arc S₁ and area of circular segment S₂. Radius of the circle is 11 and corresponding angle is ?.
Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m² . Determine dimencions of the field.
Rainfall
Annual rainfall in our country are an average of 797 mm. How many m³ of water rains on average per hectare?
Heron backlaw
Calculate missing side in a triangle with sides 17 and 34 and area 275.
Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm².
Right triangle
Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle.
Diamond
Determine the side of diamond if its content is S = 353 cm² and one diagonal u₂ = 45 cm.
Triangle
Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
Circle
How big is area of circle if its circumference is 80.6 cm?
Black building
Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m² for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchi
Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
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.
Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
Roller
Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous than
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.
Glass mosaic
How many dm² glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.

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