# 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. Trapezoid ABCD ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD.
2. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
3. Lawns Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?
4. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area?
5. Circle - easy 2 The circle has a radius 6 cm. Calculate:
6. Angles in triangle Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees.
7. Chord distance The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
8. Circle - simple Calculate the area of a circle in dm2, if its circumference is 31.4 cm.
9. Bicycle wheel Bicycle wheel diameter is 62 cm. How many times turns the bicycle on the road 1 km long?
10. Height of the arc - formula Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
11. Draw a trapezoid Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
12. Circle from string Martin has a long 628 mm string . He makes circle from it. Calculate the radius of the circle.
13. Internal and external angles Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles.
14. Right triangle ABC Calculate the perimeter and area of a right triangle ABC, if you know the length of legs 4 cm 5.5 cm and 6.8 cm is hypotenuse.
15. Clock What distance will pass end of 8 cm long hour hand for 15 minutes?
16. Annulus Calculate the area of two circles annulus k1 (S, 3 cm) and k2 (S, 5 cm).
17. Rhombus A2p Rhombus area is 13 cm2 and its height is 5cm long . Determine a perimeter of this rhombus.
18. 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?
19. Roof tiles The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
20. Grass seeds How many kg of grass seed is needed to be sowing a circular field with a diameter of 120 meters when the 1 m2 should be used 0.8 grams seeds?

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