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. Equilateral triangle
    3angle_in_circle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
  2. Infinity
    circles-and-squares In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
  3. Triangle in circle
    triangle_in_circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
  4. Rectangle
    rectangle_inscribed_circle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
  5. Recursion squares
    squares_reccurent In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of al
  6. Garden
    garden_1 Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
  7. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
  8. Slope
    slope What is the slope of a line with an inclination 6.06 rad?
  9. Coins
    eur_coins Harvey had saved up a number of 2-euro coins. He stored coins in a single layer in a square. Left 6 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
  10. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
  11. Rhombus
    rhombus2 Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
  12. Angles
    rhombus_1 Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
  13. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will angle between the hour and minute hand 90°? Consider the continuous movement of both hands hours.
  14. Scale
    pool_1 Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
  15. n-gon
    ngon_1 Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
  16. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  17. Two squares
    squares2 Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
  18. Center
    center_triangle In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
  19. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  20. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.

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