# 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. Central park in city The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path.
2. Sides of triangle Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle.
3. Two aircraft Two planes fly to the airport. At some point, the first airplane is away from the airport 98 km and the second 138 km. The first aircraft flies at an average speed of 420 km/h, the second average speed is 360 km/h, while the tracks of both planes are perpe
4. Square Calculate the perimeter and the area of square with a diagonal length 30 cm.
5. Desribed circle to rectangle Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).
6. Rhombus If we increase the rhombus side by 2.4 cm; its perimeter is 20 cm. How long was the side of the rhombus?
7. Square s3 Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
8. Angles In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
9. Regular n-gon Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
10. Trapezium The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
11. Diagonals in diamons/rhombus Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal. Zahrada má rozměry 5m a 400cm. Kolik pletiva třeba na oplocení pozemku?
13. Map scale On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters?
14. Content area and percents Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%.
15. Tree trunk From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
16. Argicultural field Field has a rectangular shape with a width 180 m and circumference 940 m. How many hectares acreage has field?
17. Unknown number 24 I think the number: a - is the same as the square area that has the 12th circumfence. What is this number? b - its half is 7 times bigger than its quarter. Is this the number?
18. Rhombus OWES OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?
19. Triangle ABC Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction
20. Hypotenuse Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.

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