Areas of Triangles Trapezoids and Rhombi Find areas

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

Area of a Triangle h b

Area of a Triangle

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

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

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 Q N P

AREAS OF TRAPEZOIDS AND RHOMBI M b 1 N h Q b 2 P

AREAS OF TRAPEZOIDS AND RHOMBI Area of area of trapezoid MNPQ = ∆MNQ + ∆MPQ b 1 M N h Q b 2 This is the formula for the area of any trapezoid. P

Key Concept 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) Area of a Trapezoid b 1 h b 2

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 T(-3, 4) V(3, 4) 4 3 2 1 -6 Z(-5, -1) -4 -2 2 -1 -2 -3 4 6 W(6, -1)

Key Concept Area of a Rhombus A B If a rhombus has an area of A square units and diagonals of d 1 and d 2 units, then A = ½ d 1 d 2. D Example: A = ½ (AC)(BD) C

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 F(2, 7) 7 6 5 E(-1, 3) 4 G(5, 3) 3 2 1 -4 -2 2 4 -1 -2 H(2, -1) 6 8

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

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

Postulate Congruent figures have equal areas.