# Parallelogram - Construct given: base, height and side

We are given lengths: base a, height h and side b and vertex point B

1. Draw top of parallelogram:
•    Draw segment from B of length a so that |\overline{AB}| .
2. Draw height of parallelogram:
•    Draw line through B perpendicular (normal) to \overline{AB} .
•    Draw circle with center B and radius h.
•    Find intersection point of this circle and the perpendicular. Rename point H.
3. Draw base line (parallel to |\overline{AB}| )
•    Draw line through H perpendicular to the perpendicular.
4. Draw third vertex (find side)
•    Draw circle e with center B and radius b.
•    Find intersection point C of this circle and base line.
5. Draw fourth vertex
•    Draw circle f with center C and radius a.
•    Find intersection point D of this circle and base line.
6. Draw parallelogram
•    Draw segments \overline{BC} , \overline{CD} and \overline{DA} .

Check construction:

Click and drag free points A and B. ABCD should remain a parallelogram.
Click and drag sliders. ABCD should change in size, but remain a parallelogram.

Save construction.

Extras:

• Draw line segment from B to H.
• Change color and thickness/line styles of all lines in construction to make more readable.
• Write dynamic formulas for perimeter and area: Input LL=2*a+2*b (enter) and Input AA=a*h (enter).
• Write dynamic text for formulas:
"Perimeter = "+LL (enter) and "Area = "+AA (enter).

Related themes: