Please help, I’m so confused

The best value for each of the characteristics of the parabola are presented in the following table;

The table of best values of parabola characteristics

The process of obtaining the above values is shown as follows;

The given parameters are;

To justify the area of a circle, the argument Yvonne wants to use = The dissection argument

The shape to which the reassembled figure tends to approximate = A parallelogram

Description of the of the reassembled figure

The horizontal parallel sides of the parallelogram formed = The arcs of the circle

The other pair of parallel sides = The radius of the circle

The best values of the characteristics of the parallelogram given in the table are therefore found as follows;

(a) The base of the parallelogram = (1/2) the total sum of the arcs in a circle = (1/2) the circumference of the circle = π·r

∴ The base of the parallelogram = π·r

(b) The height of the parallelogram = The perpendicular distance from the tip of one of the sectors to the midpoint of the arc of the sector = The radius of the circle = r

∴ The height of the parallelogram = r

(c) The area of the parallelogram, A = The sum of the area of the sectors

A = (n × θ/360) × π·r²

Where;

n × θ = 360°

Therefore;

A = (n × θ/360) × π·r² = (360/360) × π·r² = π·r²

We have;

The area of the parallelogram, A = π·r²

The table showing the best value of each characteristics of the parallelogram is therefore presented as follows;

Learn more about geometric figures (circles, and parallelogram) here;