Areas of Parallelograms, Triangles, Trapezoids and Rhombi

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Areas of Parallelograms, Triangles, Trapezoids and Rhombi

Area of a Parallelogram If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh

Examples Let’s use the parallelogram from our previous example. 5 4 What is the height of this parallelogram? 11 It is 4 units. The height is always the perpendicular distance from one side to the opposite side. What is the base of this parallelogram? It is 11 units. The base is the one of the two sides from which the height is measured. So, A = bh A = (11 units) (4 units) = 44 units 2

Work this problem 12 in. Find the area of the parallelogram A = bh A = (12 in.) (20 in.) A = 240 in. 2

Area of a Triangle If a triangle has a base of b units, and a height of h units, then A = ½ bh. A = ½ bh A = ½ (23 ft.)(6 ft.) A = 69 ft. 2 6 ft. Height Base 23 ft.

Work this problem 7 ft. 11 ft. A = ½ bh A = ½ (11 ft.)(7 ft.) A = 38.5 square feet

Area of a Trapezoid A trapezoid has bases of b1 and b2 units, and a height of h units, then A = ½ h (b1 + b2) 8 in. base 2 or b2 height A = ½ h (b1 + b2) 7 in. A = ½ (7 in.) (15 in. + 8 in.) A = ½ (7 in.) (23 in.) base 1 or b1 A = ½ (161 in. 2 ) 15 in. A = 80.5 in. 2

Area of a Rhombus A = ½ d1 d2, where d1 and d2 are diagonals. AC = 12 in. A B A = ½ d1 d2 A = ½ (12 in.)(21 in.) BD = 21 in. D C A = ½ (252 in.2) = 126 in.2