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| Geometry
- Plane Figures Problems and Solutions |
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Plane figures, solved problems, examples |
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| 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
= ? |
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| Example:
An isosceles trapezoid with the height 5 has perpendicular
diagonals. Find the area of the trapezoid. |
| Solution: Given
h
= 5. A
trapezoid
= ? |
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| 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
= ? |
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| 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
= ? |
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| 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
= ? |
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| 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
= ? |
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| Geometry
and use of trigonometry contents - A |
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