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. Rhombus diagonal
    rhombus2_1 Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
  2. Chord - TS
    chord_TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
  3. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  4. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  5. Trapezoid ABCD v2
    trapezium_table Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?
  6. Flowerbed 2
    flowerbed Around the square flower bed in a park is sidewalk 2 m wide. The area of ​​this sidewalk is 243 m2. What is the area of the flowerbed?
  7. Bases
    trapezoids_1 The length of the bases trapezium are in ratio 4:5. Length of midline is 15. How long are the bases of a trapezoid?
  8. Circle
    circles_2 Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
  9. Flowerbed
    triangle_flowers.JPG Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
  10. Round table
    obrus-kruhovy Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
  11. Semicircle
    tales-de-mileto In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
  12. Cable car 2
    lanovka_1 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
  13. Trapezoid ABCD
    trapezoid_2 Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
  14. Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
  15. The bridge
    circle_dam Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
  16. Sector
    vysec The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
  17. Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  18. Arc
    circle_2 The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?
  19. RT 10
    triangles_rt Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
  20. Rectangles - sides
    rectangles_2 One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?

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