1. Areas of Triangles, Trapezoids, and Rhombi • Find areas of triangles. • Find areas of trapezoids and rhombi.

2. Area of a Triangle h b

3. Area of a Triangle

4. Key ConceptArea of a Triangle h b If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A = ½bh

5. Example 1Areas of a Triangles Find the area of a quadrilateral XYZW if XZ = 39, HW = 20, and YG = 21. Y 21 H X Z G 20 W

6. AREAS OF TRAPEZOIDS AND RHOMBI The formulas for the areas of trapezoids and rhombi are related to the formula for the area of a triangle. M N Q P

7. AREAS OF TRAPEZOIDS AND RHOMBI b1 M N h Q P b2

8. AREAS OF TRAPEZOIDS AND RHOMBI Area of area of area of trapezoid MNPQ = ∆MNQ + ∆MPQ b1 M N h Q P b2 This is the formula for the area of any trapezoid.

9. Key ConceptArea of a Trapezoid If a trapezoid has an area of A square units, bases b1 units and b2 units, and a height of h units, then A = ½ h(b1 + b2) b1 h b2

10. Example 3Area of a Trapezoid on the Coordinate Plane Find the area of trapezoid TVWZ with vertices T(-3, 4), V(3, 4), W(6, -1), and Z(-5, -1). 6 5 T(-3, 4) V(3, 4) 4 3 2 1 -6 -4 -2 2 4 6 -1 Z(-5, -1) W(6, -1) -2 -3

11. Key ConceptArea of a Rhombus A B If a rhombus has an area of A square units and diagonals of d1 and d2 units, then A = ½ d1d2. D C Example: A = ½ (AC)(BD)

12. Example 4Area of a Rhombus on the Coordinate Plane Find the area of rhombus EFGH with vertices at E(-1, 3), F(2, 7), G(5, 3), and H(2, -1). 8 F(2, 7) 7 6 5 E(-1, 3) G(5, 3) 4 3 2 1 -4 -2 2 4 6 8 -1 H(2, -1) -2

13. Example 5Find the Missing Measure X Y Rhombus WXYZ has an area of 100 square meters. Find WY if XZ = 10 meters. W Z

14. Example 6Find the Missing Measure Trapezoid PQRS has an area of 250 square inches. Find the height of PQRS. P 20 in. Q h S R 30 in.

15. Postulate Congruent figures have equal areas.