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

  • Area of RT
    right_triangle_sepia Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
  • Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.
  • Radius
    green_circle Determine the radius of the circle, if its perimeter and area is the same number.
  • Described
    desc_circle Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
  • Square
    square_1 Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
  • Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  • Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  • Circles
    two_circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
  • Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.
  • Tinsmith
    rury Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate?
  • Rail turn
    railroad_turn The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve.
  • Wiring
    install_pipes Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 $mm2?
  • Triangle
    triangle_circle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
  • Wheat
    field_1 The rectangle shaped field with dimensions 1268 m and 745 m harvested last year was 4959 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 4 m parallel to the side of the field 745 m, where
  • Expansion
    magnification If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
  • Floor
    map_mierka The floor area of ​​the room is 31 m2 and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75?
  • Garden
    lichobeznik_zachradka 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.
  • Rectangle
    diagonal In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  • Wire
    cu_wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
  • Cable
    wire Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

See also more information on Wikipedia.