# ISEE Upper Level Quantitative : How to find the length of the side of a trapezoid

## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Trapezoid

In the above diagram, which depicts Trapezoid  and . Which is the greater quantity?

(a)

(b) 24

(b) is the greater quantity

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(a) and (b) are equal

(b) is the greater quantity

Explanation:

To see that (b) is the greater quantity of the two, it suffices to construct the midsegment of the trapezoid - the segment which has as its endpoints the midpoints of legs  and . Since  and , the midsegment, , is positioned as follows:

The length of the midsegment is half the sum of the bases, so

, so .

### Example Question #2 : How To Find The Length Of The Side Of A Trapezoid

Figure NOT drawn to scale.

The above figure depicts Trapezoid  with midsegment , and .

Give the area of Trapezoid  in terms of .

Explanation:

The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are  and :

Therefore,

The area of Trapezoid  is one half multiplied by the height, , multiplied by the sum of the lengths of the bases,  and . The midsegment of a trapezoid bisects both legs, so , and the area is

### Example Question #255 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

The above figure depicts Trapezoid  with midsegment . Express  in terms of .