# 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. Built-up area John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
2. Glass At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m2 of glass?
3. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
4. Two forces Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
5. Rhombus Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
6. MO - triangles On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
8. 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)?
9. Perimeter and legs Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
10. Carpet The room has rectangle shape with dimensions 4 m × 3.8 m. How many meters of carpet a width of 3 need to buy to cover the entire room?
11. Trapezoid - diagonal Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
12. V-belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
13. Wire D Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
14. Triangle in circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
15. Magnification of the square If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides?
16. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
17. Train The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
18. Q-Exam If tg α = 0.9, Calculating sin α, cos α, cotg α .
19. Triangle angles The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
20. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.

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