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. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  2. Estate
    semicircle Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?
  3. Triangle TBC
    isosceles_triangle TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
  4. Wire D
    semicircle_1 Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
  5. Area of RT
    sandwich_rt In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
  6. Square 2
    square_ABCD_1 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
  7. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  8. Triangle
    eq_triangle Can be rectangular triangle equilateral?
  9. Steps
    square_diagonal_1 How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
  10. Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  11. Euclid1
    pravitko Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
  12. Euclid3
    euclid2 Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
  13. Square
    square_1 Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
  14. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  15. Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  16. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  17. Midpoints
    sierpinski_1 Triangle whose sides are midpoints of sides of triangle ABC has a perimeter 45. How long is perimeter of triangle ABC?
  18. Movement
    peleton From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
  19. Circles
    two_circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
  20. Compass
    wind_rose What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?

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