Parabola in Parallelogram Parabola in Parallelogram Parabola in

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram 1. Determine the equation of the parabola

Parabola in Parallelogram

Parabola in Parallelogram 3. Determine the tangent point where the lower dashed line meets the parabola

Parabola in Parallelogram 4. Determine the height of the parallelogram

Parabola in Parallelogram 5. Determine the areas

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram

Parabola in Parallelogram The vertical distance between the dashed parallel lines has not changed so the area of the parallelogram has not changed. So neither has the ratio of the area of the blue- and yellowshaped areas. Imagine the original rectangle chopped into vertical slices that slide under the shear – each slice has not changed length and so the area has not changed.

Parabola in Parallelogram So where does this all leave us? Knowing that the parallelogram you were given could have been transformed to a rectangle you could have made your analysis and integration much, much easier!

Parabola in Parallelogram So where does this all leave us? Knowing that the parallelogram you were given could have been transformed to a rectangle you could have made your analysis and integration much, much easier!

Parabola in Parallelogram

One final thought… How could you do it without integration?

Let’s work out the area of the blue segment by a series of approximations

Note to Teacher •

RESOURCES

Parabola in Parallelogram A SIC_30

Parabola in Parallelogram B SIC_30

Parabola in Parallelogram C SIC_30

Parabola in Parallelogram D SIC_30

Parabola in Parallelogram E SIC_30

Parabola in Parallelogram F SIC_30

Parabola in Parallelogram G SIC_30

Parabola in Parallelogram H SIC_30

Parabola in Parallelogram I SIC_30

Parabola in Parallelogram J SIC_30

Parabola in Parallelogram K SIC_30

Parabola in Parallelogram L SIC_30

Parabola in Parallelogram M SIC_30

Parabola in Parallelogram N SIC_30

Parabola in Parallelogram O SIC_30

Parabola in Parallelogram P SIC_30

Parabola in Parallelogram SIC_30 Q

Parabola in Parallelogram SIC_30 R

Parabola in Parallelogram SIC_30 S

Parabola in Parallelogram SIC_30 T