# 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. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
2. The farmer The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
3. Right triangles How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality). What is the slope of a ladder 6.2 m long and 5.12 m in height.
5. Quatrefoil Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
6. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
7. Circle - easy 2 The circle has a radius 6 cm. Calculate:
8. Four circles 1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
9. Two cyclists Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
10. Garden Rectangular garden 31 meters 40 centimeters long and 20m30cm wide adjacent with the shorter side with another (fenced) garden and on one longest side is 1 meter wide gate. How many meters of fence is needed to buy? (Estimate, calculate, verify a test ca
11. Cablecar Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
12. Athlete How long length run athlete when the track is circular shape of radius 120 meters and an athlete runs five times in the circuit?
13. Pulley On wheels with a diameter of 40 cm is fixed rope with the load. Calculate how far is load lifted when the wheel turns 7 times?
14. Octagonal mat Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
15. Mirror How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
16. Internal angles One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles.
17. Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
18. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
19. Length IT Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
20. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.

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