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
(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 #1 : 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 .
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 #51 : Quadrilaterals
The above figure depicts Trapezoid with midsegment . Express in terms of .
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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