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. Largest angle of the triangle
    obtuse_triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
  2. A bridge
    arc123 A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
  3. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  4. Equilateral triangle
    equilateral_triangle2_1 Calculate the area of an equilateral triangle with circumference 72cm.
  5. Rhombus 29
    rhombus3_2 One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
  6. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  7. Map scale
    mapa_14 The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
  8. Painters
    malovka2_3 Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
  9. A rectangular
    garden_19 A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden.
  10. Perimeter of a rectangle
    rectangle_4 If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
  11. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  12. Complementary angles 2
    complementary_angles Two complementary angles are (x+4) and (2x - 7) find the value of x
  13. Ruler and compass
    triangle_bac Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
  14. Equilateral triangle
    vpisany_stvorec A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
  15. Coordinate axes
    tr_triangle_axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
  16. Construct
    kosodlznik3 Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
  17. Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
  18. Table
    stol_1 Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm.
  19. Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  20. Rectangle area
    rectangles_5 The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?

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