# Diagonal + square root - examples

1. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
2. Rhombus
Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
3. Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
4. Rhombus ABCD
Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
5. Diagonal
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
6. Square diagonal
Calculate length of the square diagonal if the perimeter is 476 cm.
7. IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
8. Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
9. 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.
10. Rhombus
Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
11. Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
12. Circles
Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
13. Right trapezoid
The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg.
14. Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
15. TV diagonal
Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
16. Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
17. Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
18. Square2
Side of the square is a = 6.2 cm, how long is its diagonal?
19. Rectangle
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
20. Tiles
How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?

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