# 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. Tree trunk Calculate the average tree trunk with a circumference of 149 cm.
2. Cable car Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
3. Square and circle Into square is inscribed circle with diameter 10 cm.What is difference between circumference square and circle?
4. Trapezium Determine the height of the trapezium ABCD, which has area 77.5 cm2 and base lengths 16 cm and 15 cm. Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
6. Rhombus IV Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
7. Circles For the circle c1(S1; r1=146 cm) and c2(S2; r2 = 144 cm) is distance of centers |S1S2| = 295 cm. Determine the distance between the circles.
8. Logs The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
9. Chord - TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
10. 3-bracket 2 May be the smallest angle in the triangle greater than 40°?
11. Angles and sides of the triangle Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
12. Diagonal in rectangle In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
14. The hall The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
15. Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
16. Parallelogram - side Calculate the length of the side of a parallelogram whose area is 175 dm2 and height to that side is 24.2 dm long.
17. See harmonics It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
18. 7 triangle The triangle area is 26.7 cm2. Determine the side length l if appropriate height hl = 45.3 cm.
19. Distance Wha is the distance between the origin and the point (18; 22)?
20. Clocks What distance will describe the tip of minute hand 6 cm long for 20 minutes when we know the starting position with finally enclose hands each other 120°?

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