Geometry - Plane Figures Problems and Solutions
      Plane figures, solved problems, examples
Example:   The ratio of the radius of the incircle to the radius of the circumcircle of a right triangle with legs, a = 3 and b = 4, is?
Solution:  Given a = 3 and b = 4.    r : R = ?
 
Example:   An isosceles trapezoid with the height 5 has perpendicular diagonals. Find the area of the trapezoid.
Solution:  Given  h = 5.   A trapezoid = ?
Example:  The ratio of the radius of the incircle to the radius of the circumcircle of a regular heptagon (n = 7) is?
Solution:  Given n = 7.    r : R = ?
 
Example:   Circumference of a sector is equal to double diameter 4r of the corresponding circle. The area of the sector is?
Solution:  Given P = 4r.    A sector = ?
 
Example:   From the midpoint of the side of a square of the length 2 circumscribed is the circle of the radius 2. The area of the intersection of the square and the circle is?
Solution:  Given  a = r = 2.    A intersection = ?
 
Example:   Through the centroid of a triangle ABC, parallel to the side AB, drawn is a line l which intersects the side AC at the point A1 and the side BC at B1. If the area of the triangle ABC is AD = 27 cm2  find the area of the trapezoid ABB1A1 .
Solution:  Given  AD = 27 cm2.    A trapezoid ABA1B1 = ?
 
Geometry and use of trigonometry contents - A
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