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. Isosceles trapezoid
    lichobeznik_5 Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  2. Regular n-gon
    10gon_polygon In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
  3. Inner angles
    triangle_1111 The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
  4. A map
    mapa_1 A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
  5. Photocopier
    picture A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
  6. Type of triangle
    237_triangle How do I find the triangle type if the angle ratio is 2:3:7 ?
  7. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  8. Trapezoid - RR
    right_trapezium Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
  9. Similarity coefficient
    trig12 The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
  10. Mirror
    mirror How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
  11. Rectangle 35
    rectangles_13 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
  12. Circle and rectangle
    described_circle A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
  13. Three shapes
    three_bodies 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
  14. Square
    ctverec_1 Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
  15. Thales
    tales Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
  16. Display case
    vitrinka Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
  17. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  18. Rhombus EFGH
    kosostvorec_10 Construct the rhombus EFGH where e = 6.7cm, height to side h: vh = 5cm
  19. Diameters of circles
    circle5_1 How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
  20. Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also more information on Wikipedia.