# 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. Church tower Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
2. Painter 3 Dad want to paint wall high 250 cm wide and 230 cm with wallpaper. How many meters must buy wallpaper if wallpaper width is 60 cm?
3. Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
4. Map scale Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden?
5. 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?
6. Wall painting The wall is 4 meters wide and 2 meters high. Window in the wall has dimensions 2x1,8 meters. How many litera of color is needed to paint two-layer this walls, if the 1 m2 needs 1 liters of paint?
7. Seeds The field has a rectangular shape with dimensions of 128 m and 350 m. How many kg of seed are needed for sowing if the 1 m2 will consume 25 g of seeds?
8. Fence How many meters of fencing it is required to purchase if our garden is rectangular measuring 20 m and 180 dm.
9. Arm-leg Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm.
10. Diamond Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
11. Ratio - rectangle The rectangle has dimensions 6 cm and 9 cm. How many times increases area and its perimeter, when its dimensions increase in the ratio 5:3?
12. Matches George poured out of the box matches and composing them triangles and no match was left. Then he tries squares, hexagons and octagons and no match was left. How many matches must be at least in the box?
13. Triangle IRT In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
14. Rectangle The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
15. Railway Between points A, B, whose horizontal distance is 1.5 km railway line has 8promile climb. Between points B, C with horizontal distance of 900 m is climb 14promile. Calculate differences of altitudes between points A and C.
16. Tiles How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?
17. Rectangular triangles The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8
18. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
19. Railway Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
20. Rectangle - desc circle Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.

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