# 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. Tiler On what surface m2 tiler must lay 30 square tiles, each of which has a side 25 cm?
2. Segment in a triangle In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
3. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
4. Arc-sector arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
5. Triangle Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
6. The field The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
7. Rectangular field One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
8. Four sides of trapezoid In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
9. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
10. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
11. Obtuse angle The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
12. Velocipede The front wheel of velocipede from year 1880 had a diameter 1.8 m. If the front wheel turned again one then rear wheel 6 times. What was the diameter of the rear wheel?
13. Isosceles trapezoid What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
14. Laths There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide
15. Diamond diagonals Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
16. Pagans Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm2 of the bottom of the sheet.
17. Right triangle Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle.
18. Square ABCD Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
19. Fence How many meters of fencing it is required to purchase if our garden is rectangular measuring 20 m and 180 dm.
20. Two triangles SSA Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14

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