Chapter 10: Exploring Polygons and Area

1. Chapter 10: Exploring Polygons and Area Lesson 10-4: Area of Triangles, Rhombi, and Trapezoids p. 535-538

2. Review from Previous Class • Refer to the figure below to find each area. • ABCDEF • Shaded part of GHIE • HONMLKJI • The entire figure including the unshaded part of GHIE A B H O L G K N M C D J F E I

3. Area of a Triangle • If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then

4. Example 1 • Find each area. 4 cm 7 cm 5 cm 8 cm h 60º 4 in

5. Deriving the Area of a Trapezoid • Now, let’s use the formula for area of a triangle to derive the formula for the area of a trapezoid. • Area of a trapezoid RSTU = area of triangle RSU + area of triangle STU R S h T U

6. Deriving the Area of a Trapezoid • Area of RSTU = area of triangle RSU + area of triangle STU

7. Area of a Trapezoid • If a trapezoid has an area of A square units, bases of b units, and height of h units, then

8. Example 2 • Find the height of a trapezoid that has an area of 50 square yards and bases of 8 yards and 12 yards.

9. Area of a Rhombus • If a rhombus has an area of A square units and diagonals of d1 and d2 units, then

10. Example 3 • A rhombus with a 20-centimeter diagonal has an area of 300 square centimeters. Find the perimeter of the rhombus

11. Summary • The following chart summarizes the area formulas that we have learned thus far.

12. Homework • p. 539 #11-19