copyright©amberpasillas2010 Good morning!! Thank you for taking the opportunity to improve your grade!!! Please follow these directions: 1.Take a seat.

copyright©amberpasillas2010

Good morning!! Thank you for taking the opportunity to improve

your grade!!!

Please follow these directions:

1.Take a seat and QUIETLY review your quiz.

2.AFTER we have discussed your quiz please sign the sheet in the correct class period and

you are free to go. It’s that easy!


Standards: CCSS.6.G.1: Find the area of right triangles, and special quadrilaterals by composing into rectangles or

decomposing into triangles and other shapes.

Essential Question: How is the formula for the area of a triangle related to the formula for the area of a parallelogram?

You need your Journal, a pencil, a metric ruler and glue.


Prepare to check your own work from Monday.

5. Use the formulas to find the area and perimeter of figure a in problem 3 if s = 5 cm.

A = lw or A = bh P = 2(l + w)

6. Use the formulas find the area and perimeter of figure b in problem 3 if w = 2.5 meters.

A = lw or A = bh P = 2(l + w)


Prepare to check your own work from Monday.

P = 2(l + w)



Today we are going to learn the Area of a Triangle & Parallelogram.

Then we are going to discover the Area of a Trapezoid.


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!


Given a right triangle

Make a similar 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


AAA

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.

We since we are

finding of the area.

÷2

half

base

height

b

h



base

heighth

This holds true for any triangle.

Notice when we put two right triangles together

it made a . When we put two isosceles

triangles together it made a .

We are still finding the area so we .half

rectangle

parallelogr

divide

a

by 2

m


A triangle is half the area of a rectangle. To find the area of a triangle, you use the rectangle formula (base times height) and divide it in half.

A = base • height 2

5 m

12 m13 m

A = 5 • 122 = 30 m2

A=1

2bh

bhA=

2


11 cm

5 cm 8 cm

Perimeter

Area

P = a + b + c

1A b h2

P = 5 + 8 + 11P = 24 cm

3 cm

1A 11 32

1A 332

2A 16.5 cm

Find the perimeter and area of this triangle.


7in 2 cm

6 in 9 cm

4 m 13 mm

11 m

8mm

8mm


• Backpack. You are making a reflective patch for your backpack. The patch is a triangle with a base of 12 cm and a height of 6 cm. What is the area of the patch?


• Draw a parallelogram with a base of 5cm and a height of 3 cm in your Math journal. Note: The height is NOT the same as the width.

5 cm

3 cm







Given the formula for area of a triangle and the formula for area of a parallelogram we are going to use that information to discover the formula

for the area of a trapezoid

Watch carefully not to miss it!


This trapezoid is regular.

regular trapezoid

This trapezoid is an irregular trapezoid.

irregular trapezoid

Also known as an isosceles trapezoid


b2

b1

h

Copy that trapezoid, flip it over, and put it next to the original

b2

b1

h

Give the height, base 1 & base 2

(b1 + b2)

h

What polygon is it now?

Parallelogram


Notice that the trapezoid is half the area of the parallelogram.

(b1 + b2)

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. It takes two trapezoids to make one parallelogram.


(b1 + b2)

h

Parallelogram

Trapezoid

A = b h

Notice that the trapezoid is half the area of the parallelogram.How do we find

half the area?

2

A = (b1 + b2) • h

Hint: Think of area of a triangle.


Area of Trapezoid

2 in

6 in

3 in

A (2 6) (8) 3

2

24

2 = 12 in2

2

A = (b1 + b2) • h

3

2

4 in


Area of Trapezoid

3 m

8 m

4 m

A (3 8) (11) 4

2

44

2 = 22 m2

2

A = (b1 + b2) • h

4

2

5 m


4 in

5 in

7 in

6 in

1A (5 7) 4

2

1 2

1A (b b ) h

2

1A (12) 4

2

A 6 4 224 in

Here is another way to look at the trapezoid formula.

Instead of dividing by 2, multiply by ½


The End!Practice in your Journal!


# 1 Area of a Trapezoid

5 ft

4 ft

A = (b1 + b2) x h2

3 ft

A = (4 + 5) x 32

A = (9) x 3 2

272 = 13.5 ft2

A = (base1 + base2) x height 2

=


Area of Polygons#2

The Area of a figure is the number of square units needed to cover it.

Rectangle

45

A l w

A 5 4

A un20 2

A b h

1078

A 10 7

A un70 2

Parallelogram Triangle

58

8 5A

2

A un20 2

7 b•hA=

2


Practice

• Complete the practice worksheet. Work in your groups.

http://www.mathslideshows.com

If you have trouble viewing you need MathType software:

To see all math formulas correctly you need to install MathType software, similar to equation editor and is available for free at Design Science website .

http://www.mathslideshows.com

For more information on Math Slideshows visit: http://www.mathslideshows.com/

copyright©amberpasillas2010 Good morning!! Thank you for taking the opportunity to improve your grade!!! Please follow these directions: 1.Take a seat.

Documents

rectangle slide

w slide

nd area

perimeter area p

triangle parallelogram

area of right triangles

base height b h slide

similar triangle