1. Obj. 29 Area Formulas The student is able to (I can): Develop and use formulas for finding the areas of triangles and quadrilaterals

2. area The number of square units that will completely cover a shape without overlapping rectangle area One of the first area formulas you have formula learned 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. h A = bh b

3. We can take any parallelogram and make a rectangle out of it: parallelograms The 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. Example Find the height and area of the parallelogram. 18 10 h 6 We 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: triangles 1 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 + b2 h b2 b1 b1 h b2 trapezoids h (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. Example Find 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.