Do Now 05/02/2014Find the unknown side length in each right triangle with legs a and b and hypotenuse c.

1. a = 20, b = 21

2. 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

Tangram7 shapes that fit together to make a square…yet it turned into a type of art.

Solve a TangramA tangram is an ancient Chinese puzzle made from a square. The

pieces can be rearranged to form many different shapes.http://pbskids.org/cyberchase/math-games/tanagram-game/

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 ParallelogramThe area of a parallelogram with base b and height h is

Area=bhb= base (long side)H= height (vertical,not slanted)*Remember that rectangles and squares are also parallelograms.

Pythagorean Theorem

• If you have a right triangle, a2 + b2 = c2 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 3Find the height of a rectangle in which b = 3 in. and A = (6x² + 24x – 6) in2.

Example 4• Find the perimeter of the rectangle, in which A = (79.8x2 – 42) cm2

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 whichA = 182x2 mm2

2. the perimeter of a rectangle in which h = 8 in. and A = 28x in2

Check For understanding

3) Find the base of the parallelogram in which h = 56 yd and A = 28 yd2.

4) Find the area of a square with one side length of 4x-2 in2.

Area of Triangles and Trapezoids

•The area of a triangle or trapezoid is half the area of the related parallelogram.

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

Example 1a) Find the area of a trapezoid in which b1 = 8 in., b2

= 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 = (15x2) cm2, when h= 10x cm.

Example 3• Find b2 of the trapezoid, in which A = 231 mm2.

Check For understanding

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

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) cm2

10 minute Break

RecallThe diagonals of a rhombus and kite are perpendicular, and the diagonals

of a rhombus bisect each other.

Area: Rhombi and Kites

A= ½ d1d2

Example 1Find d2 of a kite in which d1 = 14 in. and A = 238 in2.

Example 2• Find the area of a rhombus.

Example 3Find the area of the kite

• Step 1 The diagonals d1 and d2 form four right triangles. Use the Pythagorean Theorem to find x .

Example 3 Continued

• Step 2 Use d1 and d2 to find the area. d1 =48 , d2 =42.

Warm – Up1)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 d2 of a rhombus in which d1 = 3x m and A = 12xy m2.

HomeworkPractice A 1-11( No Variables ! )

Make your own formula sheet

Do Now • 10x

)

Check Homework

Self Quiz

60 in

Bell RingerState 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•