1. CHAPTER 11
Areas of Plane Figures

2. SECTION 11-1
Areas of Rectangles

3. The area of a square is the square of the length of a side.
POSTULATE 17
The area of a square is the square of the length of a side.
A = s2

4. If two figures are congruent, then they have the same area.
POSTULATE 18
If two figures are congruent, then they have the same area.

5. POSTULATE 19
The area of a region is the sum of the areas of its non-overlapping parts.

6. The area of a rectangle equals the product of its base and height
THEOREM 11-1
The area of a rectangle equals the product of its base and height
A = bh

7. Areas of Parallelograms, Triangles, and Rhombuses
SECTION 11-2
Areas of Parallelograms, Triangles, and Rhombuses

8. THEOREM 11-2
The area of a parallelogram equals the product of a base and the height to that base.
A = bh

9. THEOREM 11-3
The area of a triangle equals half the product of a base and the height to that base.
A = ½bh

10. The area of a rhombus equals half the product of its diagonals.
THEOREM 11-4
The area of a rhombus equals half the product of its diagonals.
A = ½d1d2

11. SECTION 11-3
Areas of Trapezoids

12. THEOREM 11-5
The area of a trapezoid equals half the product of the height and the sum of the bases
A = ½h(b1 + b2)

13. Median of a Trapezoid
The segment that joins the midpoints of the legs Median = b1 + b2 2

14. Areas of Regular Polygons
SECTION 11-4
Areas of Regular Polygons

15. Center of a Regular Polygon
Is the center of the circumscribed circle

16. Radius of a Regular Polygon
Is the distance from the center to a vertex.

17. Central Angle of a Regular Polygon
Is an angle formed by two radii drawn to consecutive vertices

18. Measure of Central Angle of a Regular Polygon
Is 360/n where n is the number of sides

19. Apothem of a Regular Polygon
Is the perpendicular distance from the center of the polygon to a side

20. THEOREM 11-6
The area of a regular polygon is equal to half the product of the apothem and the perimeter.
A = ½ap

21. Circumferences and Areas of Circles
SECTION 11-5
Circumferences and Areas of Circles

22. Circumference
Is the distance around a circle
C = 2r or d

23. Area
A = r2

24. Arc Lengths and Areas of Sectors
SECTION 11-6
Arc Lengths and Areas of Sectors

25. Sector of a Circle
Is a region bounded by two radii and an arc of the circle

26. Length of a Sector
In general, if mAB = x:
Length of AB = x/360(2r)

27. Area of a Sector
Area of sector AOB = x/360(r2)

28. SECTION 11-7
Ratios of Areas

29. Comparing Areas of Triangles
If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases.

30. Comparing Areas of Triangles
2. If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights

31. Comparing Areas of Triangles
3. If two triangles are similar, then the ratio of their areas equals the square of their scale factor.

32. If the scale factor of two similar figures is a:b, then
THEOREM 11-7
If the scale factor of two similar figures is a:b, then
The ratio of the perimeters is a:b
The ratio of the areas is a2:b2

33. Geometric Probability
SECTION 11-8
Geometric Probability

34. Probability Suppose a point P of AB is picked at random. Then:
Probability that P is on AC = (length of AC)/(length of AB)
Suppose a point P of region S is picked at random. Then:
Probability that P is in region R = (area of R)/(area of S)

35. END