Different quadrilaterals have varying traits. Use what you know to identify the quadrilaterals and compare and contrast them based upon their characteristics.

Part I. Judging by appearance, classify these quadrilaterals by all applicable names.

1) Parallelogram

2) Square

3) Rectangle

4) Trapezium or Trapezoid

Step-by-step explanation:

Step 1:  

In a parallelogram  the opposite sides will be parallel and equal

Square has all sides to be equal and the angles to be right angled.

In a rectangle, the four angles should be right angled and opposite sides should be equal.

A trapezoid or trapezium is a figure in which any  of the pair of opposite sides should be parallel.

Step 2 :

1) This figure has opposite sides to be parallel and equal. Hence based on the first definition above, this is a parallelogram

Step 3 :

2) The second figure has opposite sides to be equal and the angles are of 90 degrees or  right angled. Hence this is a square based on the second definition given in step 1

Step 4 :

3) The third figure has opposite sides to be equal and the angles are of 90 degrees or right angled. Hence this is a rectangle as per the 3 rd definition given in step 1

Step 5:

4 ) This figure has the horizontal pair of opposite sides to be parallel. Hence using the 4 Th definition in step 1, we can identify this as a trapezoid or trapezium.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80