# 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. Circle chord Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle. 5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises?
3. Garden The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
4. Office rent For rent 1m2 of office space is paid €165 per year. How much is the annual rent for an office as big as a football field with dimensions 71.5 m and 102.5 m?
5. Rectangle and circle The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
6. Octagon from rectangle From tablecloth rectangular shape with dimensions of 4 dm and 8 dm we cuts down the corners in the shape of isosceles triangles. It thus formed an octagon with area 26 dm2. How many dm2 we cuts down?
7. Thales Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
8. Rectangle The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
9. Chord MN Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
10. Clocks How long track travel the second hand in 46 hours, the end of which is 4 cm long.
11. Triangle SSA Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
12. Circular flowerbed Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
13. Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
14. Dig water well Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?
15. Rectangular trapezoid Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
16. Clock How long is trajectory of second hand of hours for day, if is 15 mm long?
17. Wheel How many times turns the wheel of a passenger car in one second if car run at speed 100 km/h. Wheel diameter is d = 62 cm.
18. Chord - TS v2 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
19. The carpet How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?
20. The book The book has 280 pages. Each side is a rectangle with sides 15 cm and 22 cm. a) how many leaves has the book? b) at least how many square meters of paper should be used to production this book?

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