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:

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

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

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 legsand. Sinceand, the midsegment,, is positioned as follows:

Trapezoid

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

, so.

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

Trapezoid 1

Figure NOT drawn to scale.

The above figure depicts Trapezoidwith midsegment., and.

Give the area of Trapezoidin 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 areand:

Therefore,

The area of Trapezoidis 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 #1 :How To Find The Length Of The Side Of A Trapezoid

Trapezoid 1

The above figure depicts Trapezoidwith midsegment. Expressin 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 areand:

The correct choice is.

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