# Pythagorean theorem - examples - page 14

1. Hexa prism Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
2. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area?
3. Catheti The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
4. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
5. Silver medal To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
6. RTriangle 17 The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
7. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
8. Cube from sphere What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
9. Perimeter of circle Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
10. Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
11. The field The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
12. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
13. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
14. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
15. Laths There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide
16. Isosceles trapezoid What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
17. Diamond diagonals Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
18. Surveyor Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?
19. Moivre 2 Find the cube roots of 125(cos 288° + i sin 288°).
20. Chord 4 I need to calculate the circumference of a circle, I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle.

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Pythagorean theorem is the base for the right triangle calculator.