Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

  1. Two lands
    pozemky The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
  2. Trapezium
    lichobeznik_3 The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm2. Calculate the length of the base and the height of the trapezoid.
  3. Quatrefoil
    4listek Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
  4. Ace
    esicko The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
  5. Equilateral triangle v3
    RRtrojuhelnik Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle.
  6. Math heart
    srdce_1 Stylized heart shape created from a square with side 5 cm and two semicircles over his sides. Calculate the content area and its circumference.
  7. Diagonals in diamons/rhombus
    diamonds Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
  8. Area and two angles
    trig_1 Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
  9. The ditch
    prikop Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
  10. Circle r,D
    bavlnka Calculate the diameter and radius of the circle if it has length 52.45 cm.
  11. 6 regular polygon
    hexagon_2 It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
  12. Complete construction
    thalet Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
  13. Arc-sector
    vzorec arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
  14. Tangents construct
    tecna The circle k is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions have the task?
  15. Chors centers
    p475_circle_tangent The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel).
  16. Inscribed circle
    Su55k02_m10 Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
  17. Rhombus
    rhombus_5 ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
  18. Outer contact of circles
    nakres_2z Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S1S2S3.
  19. Square
    percent If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
  20. Road drop
    atan On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?

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