Geometry - Plane Figures Problems and Solutions
Plane figures, solved problems, examples
Example:   The area of a circle is 6 cm2 greater then the area of the square inscribed into the circle. Then, the area of the circle is?
Solution:  Given Acircle = Asquare + 6.    Acircle = ?
Example:   Into a quarter of a circle with the radius 1 + Ö2  inscribed is a circle, find the radius of the inscribed circle.
Solution:  Given R = 1 + Ö2.    r = ?
Example:   Which polygon have two times more diagonals then sides?
Solution:  The number of diagonals in a polygon,
 where n is the number of polygon sides.
Example:   Given is a regular hexagon with the side a into which is inscribed a circle, find the area between the hexagon and the circle.
Solution:  Given a.    A = ?
Example:   If the ratio of the greater angle between diagonals of a rectangle to the smaller angle is 2 : 1 and a > b then, the ratio a : b of sides of the rectangle is?
Solution:  Given  j : (180° - j) = 2 : and  a > b.    a : b = ?
Example:   Into a circle inscribed is deltoid (kite). If one of its angles between equal sides subtends 60° then, the relation of the longer to the shorter diagonal is?
Solution:  Given a = 60°.    e :  f = ?
Example:   Determine the least n (the number of sides of a regular polygon), for which the interior angle of a regular polygon is greater then 163°.
Solution:  Given a > 163°.    n = ?
 The interior angle of a regular polygon,
Example:   Deltoid with sides length of 1 and 2 is inscribed into a circle. The ratio of greater to the shorter diagonal is?
Solution:  Given  a = 2  and  b = 1.    e :  f = ?
Example:   One side of a parallelogram is 4 cm, other 6 cm, and the diagonal 4Ö2 cm, length of the other diagonal is?
Solution:  Given  a = 6 cm, b = 4 cm and d1 = 4Ö2 cm  .    d2 = ?
Example:   Find the area of the rhomb (diamond) with the side of length 20 cm and the diagonal of length 32 cm.
Solution:  Given a = 20 cm and e = 32 cm.    A rhombus = ?
Example:   Length of the side of the right decagon is 12. Find the radius of its circumcircle.
Solution:  Given  n = 10 and  a = 12.    r = ?
Example:   In a circle with the radius 2 cm, on its chord 2Ö2 cm long taken as a diameter, constructed is another circle. The area of the part of that circle, which is outside of the greater circle, is?
Solution:  Given r = 2 cm and t = 2Ö2 cm.    A = ?
Geometry and use of trigonometry contents - A