# Diagonal + Pythagorean theorem - problems

1. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
2. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
3. Body diagonal
Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
4. Bricklayer
How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420?
5. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
6. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
7. Rhombus
Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
8. Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
9. Rhombus ABCD
Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.
10. Diagonal
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
11. Square diagonal
Calculate length of the square diagonal if the perimeter is 304 cm.
12. 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.
13. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
14. Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
15. Rhombus and inscribed
Rhombus has side a = 42 cm, the radius of the inscribed circle is r = 18 cm. Calculate the length of its two diagonals.
16. Infinity
In a square with side 9 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.
17. 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.
18. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
19. Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
20. Square diagonal
Calculate the length of diagonal of the square with side a = 4 cm.

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Pythagorean theorem is the base for the right triangle calculator.