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

2. Area of a Triangle b h

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

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. MN QP

7. AREAS OF TRAPEZOIDS AND RHOMBI h b2b2 b1b1 MN QP

8. h b2b2 b1b1 MN QP Area ofarea ofarea of trapezoid MNPQ = ∆MNQ + ∆MPQ This is the formula for the area of any trapezoid.

9. Key Concept Area of a Trapezoid h b2b2 b1b1 If a trapezoid has an area of A square units, bases b 1 units and b 2 units, and a height of h units, then A = ½ h(b 1 + b 2 )

10. Example 3 Area 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 4 3 2 1 -2 -3 -6-4-2246 T(-3, 4)V(3, 4) W(6, -1) Z(-5, -1)

11. Key Concept Area of a Rhombus AB DC If a rhombus has an area of A square units and diagonals of d1 and d2 units, then A = ½ d 1 d 2. Example: A = ½ (AC)(BD)

12. Example 4 Area 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 7 6 5 4 3 2 1 -2 -4-22468 F(2, 7) G(5, 3) H(2, -1) E(-1, 3)

13. Example 5Find the Missing Measure XY WZ Rhombus WXYZ has an area of 100 square meters. Find WY if XZ = 10 meters.

14. Example 6Find the Missing Measure Trapezoid PQRS has an area of 250 square inches. Find the height of PQRS. PQ SR 30 in. 20 in. h

15. Postulate Congruent figures have equal areas.