# Pythagorean theorem - problems - page 20

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. Square
Calculate the perimeter and the area of square with a diagonal length 30 cm.
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. Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
5. Pyramid four sides
In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
6. Wall diagonal
Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
8. Square s3
Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
9. 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.
10. 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?
11. 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.
12. Rhombus OWES
OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?
13. 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.
14. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
15. RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
16. Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
17. Two aircraft
From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour.
18. Stairway
Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
19. Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
20. A mast
A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?

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