Do Now 05/02/2014 Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = b = 21, c = 35

9.1 Developing Formulas for Triangles and Quadrilaterals Objective: Develop and apply the formulas for the areas of triangles and special quadrilaterals.

Let’s Talk Common Sense Area

Tangram 7 shapes that fit together to make a square…yet it turned into a type of art.

Solve a Tangram A tangram is an ancient Chinese puzzle made from a square. The pieces can be rearranged to form many different shapes. FOX How Would we find the area of the whole Fox?

Area Addition Postulate The area of a region is equal to the sum of the areas of its non- overlapping parts

Recall that a rectangle with base b and height h has an area of A = bh.

Area of a Parallelogram The area of a parallelogram with base b and height h is Area=bh b= base (long side) H= height (vertical,not slanted) *Remember that rectangles and squares are also parallelograms.

Pythagorean Theorem If you have a right triangle, a 2 + b 2 = c 2 where c is the hypotenuse

Example 1: Find the area

Example 2: Find the area of the parallelogram Step 1: Use the Pythagorean Theorem to find the height h. Step 2 Use h to find the area of the parallelogram

Example 3 Find the height of a rectangle in which b = 3 in. and A = (6x² + 24x – 6) in 2.

Example 4 Find the perimeter of the rectangle, in which A = (79.8x 2 – 42) cm 2 Step 1 Use the area and the base to find the height. Step 2 Use the base and the height to find the perimeter.

Check For Understanding Find each measurement. 1. the height of the parallelogram, in which A = 182x 2 mm 2 2. the perimeter of a rectangle in which h = 8 in. and A = 28x in 2

Check For understanding 3) Find the base of the parallelogram in which h = 56 yd and A = 28 yd 2. 4) Find the area of a square with one side length of 4x-2 in 2.

Area of Triangles and Trapezoids The area of a triangle or trapezoid is half the area of the related parallelogram.

Area: Triangles and Trapezoids A= ½ bh A=½(B1+B2)H

Example 1 a)Find the area of a trapezoid in which b 1 = 8 in., b 2 = 5 in., and h = 6.2 in. b) Find the area of a triangle where b= 2x and h= 25

Example 2 Find the base of the triangle, in which A = (15x 2 ) cm 2, when h= 10x cm.

Example 3 Find b 2 of the trapezoid, in which A = 231 mm 2.

Check For understanding 1) Find the area of the triangle. ( use Pythagorean THM. to find b 1 st )

Check For understanding 2) Find the area of the trapezoid 3) Find the base of a triangle in which h = 8 cm and A = (12x + 8) cm 2

10 minute Break

Recall The diagonals of a rhombus and kite are perpendicular, and the diagonals of a rhombus bisect each other.

Area: Rhombi and Kites A= ½ d 1 d 2

Example 1 Find d 2 of a kite in which d 1 = 14 in. and A = 238 in 2.

Example 2 Find the area of a rhombus.

Example 3 Find the area of the kite Step 1 The diagonals d 1 and d 2 form four right triangles. Use the Pythagorean Theorem to find x.

Example 3 Continued Step 2 Use d 1 and d 2 to find the area. d 1 =48, d 2 =42.

Warm – Up 1)Identify the base and height of the parallelogram b=h= 2)Find the area of the parallelogram 5x+4 in. 12 x in.

Check For Understanding

Check For Understanding 3) Find the d2 of the rhombus. 4) Find d 2 of a rhombus in which d 1 = 3x m and A = 12xy m 2.

Homework Practice A 1-11( No Variables ! )

Make your own formula sheet

Do Now 10x )

Check Homework

Self Quiz 60 in

Bell Ringer State the area formulas for quadrilaterals and triangles in the grid on your worksheet.

Angry Area

Rules -Each question is worth 100 points -When your team has an answer, you are allowed to ring in once. -If you are incorrect, you lose 50 points and the remaining teams have 1 minute to answer. (keep working) - team with most points at the end wins!

1)Find each measurement The perimeter of the rectangle: ( x-1) in. ( 2x+2) in.

2)Find each measurement The area of a parallelogram in which b= (x+5)ft and h= (2x-1) ft.

3)Find each measurement 2 m

4)Find each measurement The area of the whole triangle 25 in. 17 in. 15 in. 8 in.

5) Find the measurement 4 cm. 10 cm.

6) Find the measurement The area of a trapezoid : 20 m. 15 m. 9 m.

7) Find the measurement The area of a triangle in which b= (x+1) ft and h= 8x ft

8) Find the measurement 2x ft.

9) Find the measurement 6x ft.

10 ) Find the measurement