Planimetrics + diagonal - practice problems - last page
Number of problems found: 312
- Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals. - A rhombus
A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and a long side. - Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ
- ABCDEFGHIJKL 8426
The given is a regular hexagonal prism ABCDEFGHIJKL, which has all edges of the same length. Find the degree of the angle formed by the lines BK and CL in degrees. - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Diamond ABCD
In the diamond ABCD, the diagonal e = 24 cm, and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases.
- Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD? - Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Rhombus
Internal angles of a rhombus are in ratio 2:3. How many times is the shorter diagonal longer than the side of the rhombus?
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