### All ISEE Upper Level Quantitative Resources

## 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

**Possible Answers:**

**Correct answer:**

(b) is the greater quantity

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 .

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find The Length Of The Side Of A Trapezoid

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

**Possible Answers:**

**Correct answer:**

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

The correct choice is .

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