Quadrilateral
1. Characterize the quadrilaterals:
- square
- rectangle
- rhombus
- trapezoid
2. In a rhombus with area S = 864 cm2, one diagonal is 12 cm shorter than the other.
In the rhombus, the diagonals are u1 = 48 cm, u2 = 36 cm.
Side a = 30 cm.
3. A rectangle has a perimeter O = 46 cm and a diagonal u = 17 cm.
4. A rhombus has diagonals u1 = 6 cm, u2 = 8 cm.
5. A regular hexagon is inscribed in a circle with radius r.
What is the side length of a regular hexagon whose area is S = 93.42 cm2?
6. An isosceles trapezoid has a lower base c = 2.9 cm, height v = 7.5 cm, and angle α = 35°.
7. Trapezoid ABCD has an area S = 7.2 cm2, bases AB = 1.4 cm, CD = 0.6 cm.
8. The height and parallel sides of a trapezoid are in the ratio v:a:c = 2:3:5, and its area is S = 512 cm2.
9. A rectangle has a diagonal u = 34 cm. If each of its sides is increased by 4 cm, its area increases by 200 cm2.
10. A trapezoid has a top base c = 33 cm and height v = 15 cm. The other three sides are equal.
