# Algebraic Expressions and Geometry, grade 9, question 1

**(x>0) ;****S**represents the area of rectangle ABCD and**S’**represents the area of trapezoid EFCD.

- Express
**S**in terms of x. - Prove that
**S’**= (x+2)(6-x). - Calculate x if
**S’**= 12. - In what follows x = 2
- Calculate ED and EG.
- Verify that triangle GEF is a reduction of triangle GDC with scale factor and center to be determined.