500 likes | 626 Vues
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 = 21 2. b = 21, c = 35. 9.1 Developing Formulas for Triangles and Quadrilaterals.
E N D
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 = 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.
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. 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 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, a2 + b2 = c2 where c is the hypotenuse
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) 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 which A = 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.
Example 1 • 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
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 d1d2
Example 1 Find d2 of a kite in which d1 = 14 in. and A = 238 in2.
Example 2 • Find the area of a rhombus.
Example 3 Find 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 – Up 1)Identify the base and height of the parallelogram b= h= 2)Find the area of the parallelogram 12 x in. 5x+4 in.
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.
Homework Practice A 1-11( No Variables ! )
Do Now 10x )
Self Quiz 60 in
Bell Ringer State the area formulas for quadrilaterals and triangles in the grid on your worksheet.
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: ( 2x+2) in. ( x-1) in.
2)Find each measurement The area of a parallelogram in which b= (x+5)ftand h= (2x-1) ft.
4)Find each measurement The area of the whole triangle 25 in. 17 in. 15 in. 8in.
5) Find the measurement 10 cm. 4cm.
6) Find the measurement The area of a trapezoid : 15 m. 20 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 6xft.