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 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.
  2. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  3. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  4. Jewel
    rhombus3 Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
  5. 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.
  6. RT - hypotenuse and altitude
    pravy_trojuholnik Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
  7. Square
    1square Calculate area of the square with diagonal 64 cm.
  8. Rectangles
    strihanie Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
  9. Circle and angle
    arc What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
  10. Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
  11. Slope
    slope What is the slope of a line with an inclination 6.06 rad?
  12. Circle
    kruznica Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  13. Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  14. Garden
    garden Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
  15. KLMN
    trapezium In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
  16. Rhombus
    rhombus_3 Find the length of each side of rhombus if the perimeter is 49 dm long.
  17. 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?
  18. Hexagon - MO
    6uholnik_nepravidelny The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|
  19. Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  20. n-gon
    x-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?

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