2Area Of Parallelograms Definition:A parallelogram is a quadrilateralwith opposite sides parallel.
3Review of Characteristics of Parallelograms Opposite sides are parallel.Consecutive angles aresupplementary. (SSI angles)Opposite sides are congruent.Opposite angles are congruent.
4Review of Characteristics of Parallelograms Opposite sides are parallel.Consecutive angles aresupplementary. (SSI angels)Opposite sides are congruent.Opposite angles are congruent.Diagonals bisect each other.
5Areas of Parallelograms Find the area by counting squares.8Full blocks =4Half blocks =Total Area =10 su.
6Areas of Parallelograms Find the area by counting squares.Full blocks =12Half blocks =6Total Area =15 su.
7Areas of Parallelograms Find the area by counting squares.20Full blocks =8Half blocks =Total Area =24 su.
8There is!!! Don’t you agree? ? ? There must be ? ? an easier way! ? ? It is tough to computeall the partial blocks.??There must bean easier way!????There is!!!??I like rectangles much better!They are real easy!Don’t you agree?
9Let’s cut off a corner and start to make a rectangle. Doesn’t a parallelogram looklike a rectangle with it’s side kicked in?Let’s cut off a corner andstart to make a rectangle.
10Wow! We have part of a rectangle. Now watch what else we have.
11Let’s move the triangle to the other side. The two triangles are congruent.Let’s move the triangle to the other side.
12What has happened?We have now createda rectanglewith the same areaas the parallelogram.
13We have now createda rectanglewith the same areaas the parallelogram.Therefore,the formula for the areaof a parallelogramis the sameas that of a rectangle.
33Find the base associated with the corresponding height. Triangle ABC has three altitudes or heights.They are …Each side is a corresponding base.Find the base associated withthe corresponding height.
34h h If the area = 96 and …. Find the values of AD and FC. This is a backwards problem.You always startwith the formula.h
35h h If the area = 96 and …. Find the values of AD and FC. This is a backwards problem.You always startwith the formula.h
36Backward Problems 2 2 h 25 h 125 25 If the area is 125 sf, and the base is 25, find the height.h2225Divide by 25h12525
37182 h 30 30 h If the area is 182 sf, and the base is 30, find the height.h3018230h
38Compound Complex Multiple Stage Problems With these problems, you…1 Plan solution with equations or written strategyas if you have all the information needed.2. Write the equation, leaving empty parenthesesto insert the needed values.3. Go find the needed values in sidebar stages,substituting back into the original strategy or equation.4. When all values are found,complete the original strategy or equation.
50Summary 1. The area of a parallelogram is… 2. The area of a triangle is half the area of parallelogram.3. A triangle has three heights or altitudes.4. A triangle has three bases (sides)to correspond with each height.