# Diagonal - problems

- Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - KLMN trapezoid

In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line. - Diagonals of pentagon

Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm. - 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? - 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. - Rectangle

The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 38 cm and 55 cm long. - Logs

Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Rhombus ABCD

Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm. - Square diagonal

Calculate length of the square diagonal if the perimeter is 304 cm. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees. - 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. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - 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. - Rectangle

In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - 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.

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