# 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. Rotatable tower Rotatable tower situated in the city center has ground shape of a regular polygon. If the tower is rotated by 14.4° around its centerpiece it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view of the.
2. Trio 2 Decide whether trio of numbers is the side of a right triangle: 26,24,10.
3. 2d shape Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm. Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
5. Plot The plot on which Mr. Kalous is to build a house has the shape of a rectangle. On a 1: 500 scale, its dimensions are 7cm and 5.5cm. Find out the dimensions of the plot. Calculate the parcel size.
6. Regular octagon Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
7. Four ropes TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
8. Centre of mass The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
9. Diameters of circles How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
10. Cableway Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
11. Rounding What width and length in centimeters may have rectangle land when round the dimensions to the meter , the width is 5 m and length 7 meters?
12. Diagonals of diamond Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
13. Isosceles trapezoid Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
14. Parallelogram In the parallelogram we know one internal angle 67°33`. Calculate the other internal angles.
15. Is right triangle Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
16. Ruler How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
17. 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.
18. Land - isosceles trapezoid Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
19. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree? A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?