 # Copyright©amberpasillas2010. Perimeter – (P) (P) The distance around a figure. 10 ft. 6 ft. 10 6 + 36 ft.

## Presentation on theme: "Copyright©amberpasillas2010. Perimeter – (P) (P) The distance around a figure. 10 ft. 6 ft. 10 6 + 36 ft."— Presentation transcript:

Perimeter – (P) (P) The distance around a figure. 10 ft. 6 ft. 10 6 + 36 ft.

copyright©amberpasillas2010 PERIMETER: Is the distance around a figure. When you add the sides you are adding the units. When you add units, your units DO NOT CHANGE! If this rectangle has units in inches, then you are adding in + in + in + in = in You must include units in every answer!

copyright©amberpasillas2010 The Area o f a figure is the number of square units n eeded to cover it. A = 2 3 A = 6 square units A = 6 units 2 2 3

PERIMETER: Is the distance around a figure. in + + + = AREA: Is the square units that cover a figure. length width= in in = in 2 VOLUME: The number of cubic units inside a figure. length width height in in in = in 3 length width height squared cubed width copyright©amberpasillas2010

8 m 6 m A = 8 6 2 = 24 m 2 A = base height 2 A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half. 5 m

copyright©amberpasillas2010 5 in 3 in A = b h A = 5 3 = 15 in 2 To find the area for a parallelogram use what you know about area of a rectangle. A = base height 4 in

copyright©amberpasillas2010 6 ft 3 ft A = (b 1 + b 2 ) h 2 4 ft A = (3 + 6) 4 2 A = (9) 4 2 = 36 2 = 18 ft 2 A = (base 1 + base 2 ) height 2 5 ft

Perimeter & Area Review # 11 The Area (A) of a figure is the number of square units needed to cover it. The Perimeter (P) is the distance around a figure. a b c P= a+b+c units height base (h) (b) A = 2 6 12 square units 12 units 2

9 cm 5 cm6 cm 3 cm Area & Perimeter of a Triangle # 12 Perimeter P = a + b + c P = 5 + 6 + 9 P = 20 cm Area copyright©amberpasillas2010

#13 Perimeter & Area of a Rectangle The Perimeter of a figure is the distance around a figure. 2 in. 5 in. 2 5 2 5 + 14 in. The Area of a figure is the number of square units needed to cover it. A = 3 2 6 square units 6 units 2 3 2

copyright©amberpasillas2010 Teacher Note : The following study guide slides were taken from the lesson on Perimeter and Area review under the PERIMETER FOLDER

copyright©amberpasillas2010 a b c d e f g h P=a+b+c+d+e+f+g+h a b c P= a+b+c P=4s s s s s l l w w P=2l+2w #9

copyright©amberpasillas2010 #10 Perimeter of a Triangle Perimeter : Distance around a geometric figure. When you add the sides, you are also adding the units. When you add units, your UNITS DO NOT CHANGE ! You must include units in every answer!

copyright©amberpasillas2010 #11 Perimeter of a Rectangle & Square The Perimeter of a figure is the distance around a figure. 2 in. 5 in. 2 5 2 5 + 14 in. Rectangle 4 5 8 ft Square

copyright©amberpasillas2010 Teacher Note: Extra lesson on just area formulas without the perimeter

copyright©amberpasillas2010 Area of a Rectangle Area of a Square Area of a Triangle Area of a Parallelogram Area of a Trapezoid REVIEW OF FORMULAS

copyright©amberpasillas2010 Area of a Rectangle height base (h) (b) A = bh The area of this rectangle is 8 squares, or 8 units squared Area is in units 2 because you are multiplying units.

copyright©amberpasillas2010 A square is a special rectangle Since the base and the height are the same size, we call them sides (s) instead of base and height. s height = s s base = s A= s 2 Area of a Square

copyright©amberpasillas2010 What is the area of the square? 4 m. 4 4x 16m. 2 16 m 2 or square meters Area of a Square

copyright©amberpasillas2010 Area of a Triangle Given the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle. Watch carefully not to miss it!

copyright©amberpasillas2010 Area of a Triangle Given a right triangle Make a similar triangle,

copyright©amberpasillas2010 Area of a Triangle Given a right triangle Make a similar triangle, flip it and put both triangles next to each other What polygon is this? A Rectangle

copyright©amberpasillas2010 Area of a Triangle What is the formula for the area of a triangle ? We can use the formula for area of a rectangle to find the formula for area of a triangle. Two triangles make one rectangle. We want to find half of the area of the rectangle. base height b h

copyright©amberpasillas2010 Area of a Triangle base height h This holds true for any triangle

copyright©amberpasillas2010 Draw a straight line from the top corner perpendicular to the base Cut that triangle and move it to the other side What shape does it make? Rectangle Area for a Parallelogram

copyright©amberpasillas2010 What is the formula for area of a parallelogram? A parallelogram has the same area as a rectangle h base = b height = h h b Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Check to see if you got it right. Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line. Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line. Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side. Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side. Area for a Parallelogram

copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Now you have a rectangle A = 8 square cm. or 8 cm. 2 Let’s check it with the area of a rectangle. How many squares do you see? Area for a Parallelogram

copyright©amberpasillas2010 b1b1 b2b2 h Copy that trapezoid, flip it over, and put it next to the original b1b1 b2b2 h Given the height, base 1, and base 2 (b 1 + b 2 ) h What shape is it now? Parallelogram Area of a Trapezoid

copyright©amberpasillas2010 Notice that the trapezoid is half the area of the parallelogram. It takes two trapezoids to make one parallelogram. (b 1 + b 2 ) h Given our original trapezoid Put together with a similar flipped trapezoid, we found it made a parallelogram. We are going to use the area of a parallelogram to find the area of a trapezoid. Area of a Trapezoid

copyright©amberpasillas2010 (b 1 + b 2 ) h Parallelogram Trapezoid A = (b 1 + b 2 ) 2 Area of a Trapezoid

copyright©amberpasillas2010 Area of Trapezoid A = (b 1 + b 2 ) 2 2 in 6 in 3 in = 12 in 2 Area of a Trapezoid