# Planimetrics - 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. KLM triangle Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
2. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
3. The size The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side.
4. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
6. An angle An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
7. A large A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
8. Lake or pond The landlord has a square lake. Trees grow around this lake. The lake wants to enlarge the pond twice and does not want to cut down or flood any tree. How will he do that?
9. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
10. Rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
11. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
12. Rectangular field A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
13. Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
14. Two gears The two gears fit together. The larger gear has 32 teeth, the smaller has 20 teeth less. How many times does turn a smaller gear if the bigger gear turns three times?
15. Three segments The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
16. Area to perimeter Calculate circle circumference if its area is 254.34cm2
17. Each with each Five pupils from 3A class played table tennis. How many matches did they play with each other?
18. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
19. Screens The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
20. Equation - inverse Solve for x: 7: x = 14: 1000

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