
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 A_{1}
and the side BC
at B_{1}. If the area of the triangle
ABC
is A_{D}
= 27 cm^{2}
find the area of the trapezoid ABB_{1}A_{1} . 
Solution: Given
A_{D}
= 27 cm^{2}.
A
_{trapezoid
}_{ABA}_{1}_{B}_{1}
= ? 









Geometry
and use of trigonometry contents  A 





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