# 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. Diagonals in the diamond The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
2. Leg Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
3. Triangle SAA The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
4. Isosceles trapezoid The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
5. Chord AB What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
6. Circle arc Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
7. Around the flowerbed Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros
8. Snowman 2 On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express
9. Circular motion Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
10. Segment Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
11. Rectangular trapezoid How many inner right angles has a rectangular trapezoid?
12. Parallelogram The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
13. Trapezoid RT The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
14. Rectangular trapezoid The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
15. Rhombus problem Perimeter of the rhombus is 204 dm and it area is 2244 dm2. Calculate the height of the rhombus.
16. Earth's diameter The Earth's diameter on the equator is approximately 12750 km. How long does the Gripen flyover the Earth above the equator at 10 km if it is at an average speed of 1500 km / h?
17. Circumscription Calculate radius of the Circumscribed circle in the rectangle with sides 20 and 19. It can be rectangle inscribed by circle?
18. Goniometric form Determine goniometric form of a complex number ?.
19. Trapezoid ABCD v2 Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?
20. Diamond Determine the side of diamond if its content is S = 353 cm2 and one diagonal u2 = 45 cm.

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