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. Circle
    circles From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
  2. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
  3. Rhombus
    rhomus_circle It is given a rhombus of side length a = 19 cm. Touch points of inscribed circle divided his sides into sections a1 = 5 cm and a2 = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  4. Rectangle
    rectangle_ABCD In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
  5. Rectangle vs square
    squares_3 The rectangle has dimensions of 13 × 10, square 8 × 8. Which shape has more area and how much above?
  6. Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.
  7. Windows
    wall_w_windows Calculate the area of masonry to build wall with dimensions of 9 m × 4 m with 4 windows of size 64 cm × 64 cm.
  8. Carpet
    koberec The room has rectangle shape with dimensions 4 m × 3.8 m. How many meters of carpet a width of 3 need to buy to cover the entire room?
  9. Right Δ
    ruler A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
  10. 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.
  11. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  12. Area 4gon
    4gon Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
  13. Radians
    pi_text Convert 270° to radians. Write result as multiple of number π.
  14. Hypotenuse and height
    euklides In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
  15. Radius
    green_circle Determine the radius of the circle, if its perimeter and area is the same number.
  16. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  17. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  18. Arc
    arc_1 Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
  19. Described
    desc_circle Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
  20. Intersections
    intersect_circles How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.

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