1. CHAPTER 11
By Trey Mourning and Hallie Meland

2. Sections
11.2: Areas of Parallelograms, Rectangles, and Triangles
11.1: Areas of Rectangles
11.3: Areas of Trapezoids
11.4: Areas of Regular Polygons

3. How to find the area of squares and rectangles
The area of a rectangle equals the product of its base and height
A= bh
Square:
The area of a square is the square of the length of a side (A=s2)
Note: if two figures are congruent, then they have the same area

4. Find the area of: 15 3 7 10 4 6 15 3 A 3 Area of A = (3)(15) = 45
Area of B = (4)(6) = 24
Area of C = (3)(2) = 6
Area of the Whole = A+B+C
Area of the Whole=
Area of the Whole = 75 7 4 B 4 6 3 C 2

5. Area addition postulate
The area of a region is the sum of the areas of its non-overlapping parts
Find the area of: 15 3 10 7 4 6

6. How to find the area of Parallelograms and Rhombuses
The area of a parallelogram equals the product of a base and the height to that base
A= bh
Rhombus:
The area of a rhombus equals half the prodcut of its diagonals
A= ½(d₁d2 ₂)
Find the area of this rhombus 5 4

7. How to find the area of a Triangle
The area of a triangle equals half the product of a base and the height to that base
½bh
If the triangle is equilateral then the formula
√3/4 s2 can be used to determine the area 10 10 6 6
Find the area of these triangles 16 6

8. How to find the area of a trapezoid
The area of a trapezoid equals half the product of the height and the sum of the two bases
Half of the sum of the two bases is equal to the median of the trapezoid, therefore there are to formulas that can be used
A= ½(b₁+b ₂)h OR A= mh 12 8 8
Find the area of this isosceles trapezoid 60

9. How to find the area of a regular polygon
Center of a regular polygon: the center of the circumscribed circle (O)
Radius of a regular polygon: the distance from the center to a vertex (OA, OB, OC, etc)
Central angle of a regular polygon: an angle formed by two radii drawn to consecutive vertices (AOB, BOC, etc)
Apothem of a regular polygon: The (perpendicular) distance form the center of the polygon to a side (OX) D
O  C A X B

10. How to find the area of a regular polygon
The area of a regular polygon is equal to half the product of the apothem and the perimeter
A=½aP
Regular hexagon with sides of 8
Regular pentagon with sides of 8
Find the area, apothem, and perimeter of the following regular polygons

11. Find the area of a regular hexagon with apothem 9
Find the measure of angles of the traingle
Use the newly found relationship to find the values of the other sides
½S = 9/√3 = 3√3
S = 6√3
P = 36√3
Area = ½ap
½ (9)(36√3)
A = 162√3
30* ½S

12. Section 11.5
Circles

13. Circumference and Area of Circles
Circum.= 2πr also Circum.= πd
Area= πr2
Circumference of a circle:
Area of a Circle:
Find the area of the given circle
find the circumference of the given circle

14. Section 11.6
Arcs and Sectors

15. Arc Lengths and Areas of Sectors
A sector: a region bounded by two radii and an arc of the circle
find the arc length and the area of the sector

16. Chapter 11.7
Ratios

17. Ratios of Areas
Theorem 11-7: if the scale factor of two similar figures a:b then…
1. the ratio of the perimeters/circumferences and sides is a:b
2. the ratios of the areas is a2:b2
Find the value of x 15 4 5 12 3 x