# 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. V-belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
2. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
3. Equilateral triangle Calculate the side of an equilateral triangle, if its area is 892 mm2.
4. Heron backlaw Calculate missing side in a triangle with sides 17 and 34 and area 275.
5. Diamond Determine the side of diamond if its content is S = 353 cm2 and one diagonal u2 = 45 cm.
6. Track arc Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
7. Circle How big is area of circle if its circumference is 80.6 cm?
8. ABS CN Calculate the absolute value of complex number -15-29i.
9. Chord MN Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
10. Median The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
11. Steeple Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
12. Cable car Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
13. Circle On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
14. Shooter The probability that a good shooter hits the center of the target circle I is 0.1. The probability that the target hit intercircle is II 0.58. What is the probability that it hits the target circle I or II?
15. Isosceles right triangle Calculate the area of an isosceles right triangle whose perimeter is 377 cm. Road sign informs the gradient is 10.3%. Calculate the angle which average decreases.
17. Black building Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchi
18. Right triangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
19. Circle and angle What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
20. Magnification of the square If we increase the square side, increase the content of the 94 %. About what percentage was increased his sides?

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