# 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. AP RT triangle The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
2. Two chords There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
3. Trapezium diagonals It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
4. Horizontal distance The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
5. Irrigation sprinkler The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate?
6. In the In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
7. On line On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
8. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5).
9. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
10. Square Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm2.
11. Sum of inner angles Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
12. Map scale 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?
13. Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
14. Isosceles triangle 8 If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
15. Circular arc Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 °
16. Diagonals of the rhombus How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
17. Triangles Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different trian
18. Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
19. 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.
20. 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.

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