Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms People work with areas in many occupations: Carpenters calculate the areas of walls, floors, and roofs before they purchase materials for construction. Painters calculate surface areas so that they know how much paint to buy for a job. Decorators calculate the areas of floors and windows to know how much carpeting and drapery they will need. OBJECTIVE: In this chapter you will discover formulas for finding the areas of the regions within: triangles parallelograms trapezoids kites regular polygons, and circles. JRLeon Geometry Chapter 8.1 HGSH

Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms The area of a plane figure is the measure of the region enclosed by the figure. You measure the area of a figure by counting the number of square units that you can arrange to fill the figure completely. RECTANGLE: Any side of a rectangle can be called a base. A rectangle’s height is the length of the side that is perpendicular to the base. For each pair of parallel bases, there is a corresponding height. If we call the bottom side of each rectangle in the figure the base, then the length of the base is the number of squares in each row and the height is the number of rows. JRLeon Geometry Chapter 8.1 HGSH

Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms EXAMPLE A: Find the area of this shape. 3x2/2 5x2/2 2x3/2 6x3/2 3x2 5x2 2x3 6x3 8x4 3𝑥2 2 + 5𝑥2 2 + 2𝑥3 2 + 6𝑥3 2 + 8𝑥4 3+5+3+9+32 = 52 JRLeon Geometry Chapter 8.1 HGSH

Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms Parallelogram Just as with a rectangle, any side of a parallelogram can be called a base. But the height of a parallelogram is not necessarily the length of a side. An altitude is any segment from one side of a parallelogram perpendicular to a line through the opposite side. The length of the altitude is the height. The altitude can be inside or outside the parallelogram. No matter where you draw the altitude to a base, its height should be the same, because the opposite sides are parallel. JRLeon Geometry Chapter 8.1 HGSH

Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms Area Formula for Parallelograms h s b JRLeon Geometry Chapter 8.1 HGSH

Areas of Rectangles and Lesson 8.1 Areas of Rectangles and Parallelograms Area Formula for Parallelograms EXAMPLE B: Find the height of a parallelogram that has area 7.13 m2 and base length 2.3 m. A = bh A/b = h 7.13/2.3 = h 3.1 m = h JRLeon Geometry Chapter 8.1 HGSH

JRLeon Geometry Chapter 8.2 HGSH Lesson 8.2 Areas of Triangles, Trapezoids, and Kites h b1 b2 b = b1 + b2 Rectangle A1 = b1h Triangle A1 = b1h/2 Rectangle A2 = b2h Triangle A2 = b2h/2 (half the rectangle) Triangle A1 + A2 = b1h/2 + b2h/2 A = (b1 + b2)h/2 = bh/2 JRLeon Geometry Chapter 8.2 HGSH

JRLeon Geometry Chapter 8.2 HGSH Lesson 8.2 Areas of Triangles, Trapezoids, and Kites Area Formula for Trapezoids b2 b1 b2 Area of Parallelogram = bh = (b1+b2)h h b1 And dividing by 2, Therefore, the area of the Trapezoid is; = (b1+b2)h/2 JRLeon Geometry Chapter 8.2 HGSH

JRLeon Geometry Chapter 8.2 HGSH Lesson 8.2 Areas of Triangles, Trapezoids, and Kites Area Formula for Kites d1 d2 𝟐 d2 d1 Area of Rectangle = bh Area of the Kite = d1d2 𝟐 JRLeon Geometry Chapter 8.2 HGSH

JRLeon Geometry Chapter 8.1-8.2 HGSH Lesson 8.2 Areas of Triangles, Trapezoids, and Kites Class Work / Home Work: 8.1 Pages 425 – 427 : problems 1 thru 17 ODD and 21, 23 8.2 Pages 430 – 432 : problems 1 thru 21 ODD JRLeon Geometry Chapter 8.1-8.2 HGSH