# 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. Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
2. The big clock The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00.
3. Six-sided polygon In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
4. The mast The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
5. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ? The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
7. Isosceles trapezium Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
8. Tv screen The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
9. Same area There is a given triangle. Construct a square of the same area.
10. Photo frame A square shape photo with a side length of 20 cm is framed by a 4 cm wide bar. Find the external frame size of this photo (the frame is from all sides)
11. Pexeso Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?
12. If the If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
13. Calculate Calculate the length of a side of the equilateral triangle with an area of 50cm2.
14. The sides The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
15. Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
16. KLMN trapezoid 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?
17. Rectangle diagonal The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2. Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
19. RT - inscribed circle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
20. The swimmer The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion

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