Square + Pythagorean theorem - math problems

1. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
2. Tree trunk What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
3. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
4. Square Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
5. Logs Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
6. Square and circles Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
7. Square diagonal Calculate length of the square diagonal if the perimeter is 476 cm.
8. Prism Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 10 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
9. Steps How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
10. Infinity In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
11. Octagon We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
12. Recursion squares In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
13. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
14. Square diagonal Calculate the length of diagonal of the square with side a = 23 cm.
15. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
16. Square 2 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
17. Square Calculate area of the square with diagonal 64 cm.
18. MO circles Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
19. Circles Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square? I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.