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. Screens
    tv2_3 The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
  2. Triangle perimeter
    triangle_vysky_3 Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
  3. Equation - inverse
    hyperbola_3 Solve for x: 7: x = 14: 1000
  4. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  5. Depth angle
    cliff From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
  6. One trapezium
    trapezium_5 One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
  7. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  8. Infinite sum of areas
    height-of-equilateral-triangle Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr
  9. Parallelogram
    kosodlznik3_1 Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
  10. KLMN trapezoid
    lich_3 The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
  11. Land
    12-13-5-triangle Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
  12. Rectangle 45
    rectangles2_4 The perimeter of a rectangle is 60cm. If the length of the rectangle is 20cm. a)find the width b)find the area.
  13. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  14. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  15. Waste
    doska_kruh How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
  16. Flooring a room
    tiles_10 Find the cost of flooring a room 6.5 m by 5 m with square tiles of sides 25 cm at the rate of rupees 9.40 per tile.
  17. A tile
    tiles_9 A tile setter is covering 5ft by 5ft square shower wall. Each tile covers 4 5/8in by 4 5/8in square. How many rows of tile are needed to reach 5ft? How many tiles are needed to cover 5ft by 5ft square
  18. Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  19. Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  20. Cutting square
    circle22 From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?

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