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

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

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

Trapezoid

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

(a) 

(b) 24

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

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

Correct answer:

(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:

 

Trapezoid

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

Trapezoid 1

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:

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

Trapezoid 1

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

Possible Answers:

Correct answer:

Explanation:

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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