CHAPTER 11 By Trey Mourning and Hallie Meland

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

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

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= 45 + 24 + 6 Area of the Whole = 75 7 4 B 4 6 3 C 2

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

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

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

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

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

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

Find the area of a regular hexagon with apothem 9 Find the measure of angles of the traingle Use the newly found 30-60-90 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

Section 11.5 Circles

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

Section 11.6 Arcs and Sectors

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

Chapter 11.7 Ratios

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