# 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. Circular ring Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
2. The ditch Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
3. Fertilizer Meadow with an area of 1,500 square meters was fertilized with 12 kg of urea. Urea contains 45% nitrogen. How much nitrogen accounted per 1 m2?
4. Arm-leg Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm.
5. Equilateral triangle The equilateral triangle has a 23 cm long side. Calculate its content area.
6. Square Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
7. Paving - joints We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?
8. Gardens I have a garden in the shape of a square with a side length of 0.02 kilometers. Neighbor has a large garden as well and one side of the garden we share. I'd bought from a neighbor garden that my area of my garden increased to 5 ares. a/ By how many acres I
9. Candy - MO Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triang
10. Area of ditch How great content area will have a section of trapezoidal ditch with a width of 1.6 meters above and below 0.57 meters? The depth of the ditch is 2.08 meters.
11. Outer contact of circles Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S1S2S3.
12. Parallelogram Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram. Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder?
14. Hot air balloon The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the bal
15. Rectangle Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
16. Rectangle The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
17. Tiles It is given an area of 5m x 4m One tile is 40 x 40 cm How many tiles are needed in an area of 5 m x 4 m? And how many tiles need to be cut (if it not possible for the tiles to fall exactly)?
18. Trapezoid - RR Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
19. Paper squares The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
20. Air pressure The meteorological station measured the air pressure of 1060 hPa (hectopascals). In addition to measuring instruments, there is a residential house that has a flat roof with dimensions of 10 m and 28 m. What pressure force in MN (meganewtons) force the ai

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