1. Obj. 44 Triangles & Quadrilaterals The student is able to (I can): Develop and use formulas for finding the areas of triangles and quadrilaterals

2. areaThe number of square units that will completely cover a shape without overlappingrectangle area One of the first area formulas you learned formula was for a rectangle: A = bh, where b is the length of the base of the rectangle and h is the height of the rectangle.hA = bh b 3. We can take any parallelogram and make a rectangle out of it:parallelogramsThe area formula of a parallelogram is the same as the rectangle: A = bh (Note: The main difference between these formulas is that for a rectangle, the height is the same as the length of a side; a parallelograms side is not necessarily the same as its height.) 4. ExampleFind the height and area of the parallelogram. 18 10h 6We can use the Pythagorean Theorem to find the height:h = 102 62 = 8 Now that we know the height, we can use the area formula: A = ( 18 )( 8 ) = 144 sq. units 5. We can use a similar process to find out that the area of a triangle is one-half that of a parallelogram with the same height and base:triangles1 bh A = bh or A = 2 2 6. A trapezoid is a little more complicated to set up, but it also can be derived from a parallelogram: b1 + b2h b2b1b1 h b2trapezoidsh (b1 + b2 ) 1 A = h ( b 1 + b2 ) or A = 2 2 7. A rhombus or kite can be split into two congruent triangles along its diagonals (since the diagonals are perpendicular):Rhombi, squares, and kites Area of one triangle = 1 ( d1 ) 1 d2 = 1 d1d2 2 2 4 1 1 Two triangles = 2 d1d2 = d1d2 4 2 (Squares can use the same formula.) 8. ExampleFind the d2 of a kite in which d1 = 12 in. and the area = 96 in2. d1d2 A= 2 12d2 96 = 2 12d2 = 192 d2 = 16 in.