# 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. Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
2. Square garden On the plan with a scale of 1:1500 is drawn as a square garden with area 81 cm2. How many meters is long garden fence? Determine the actual acreage gardens.
3. Triangles Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
4. Broken tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
5. Tiles How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles?
6. Railway Between points A, B, whose horizontal distance is 1.5 km railway line has 8promile climb. Between points B, C with horizontal distance of 900 m is climb 14promile. Calculate differences of altitudes between points A and C.
7. Isosceles - isosceles It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
8. Right angled triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
9. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
10. Drainage channel The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
11. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
12. Percentage and rectangle About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
13. Chord distance The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
14. Trapezoid v3 The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ?
15. Diamond Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
16. Equilateral triangle v3 Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle.
17. Parcel parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel?
18. The farmer field The field has paralleogram shape with dimensions side a = 80 m and height 296 m. Two and two sides is at angle 80°. Calculate acreage of field in hectares.
19. Chors centers The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel).
20. Rectangle The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?

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

To this e-mail address, we will reply solution; 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...