How to find the length of the side of a trapezoid - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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In the above diagram, which depicts Trapezoid 
, 
and 
. Which is the greater quantity?
(a) 
(b) 24
In the above diagram, which depicts Trapezoid
(a)
(b) 24
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 
.
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
The length of the midsegment is half the sum of the bases, so
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Figure NOT drawn to scale.
The above figure depicts Trapezoid 
with midsegment 
. 
, and 
.
Give the area of Trapezoid 
in terms of 
.
Figure NOT drawn to scale.
The above figure depicts Trapezoid
Give the area of Trapezoid
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
The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are
Therefore,
The area of Trapezoid
Compare your answer with the correct one above
The above figure depicts Trapezoid 
with midsegment 
. Express 
in terms of 
.
The above figure depicts Trapezoid
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 
.
The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are
The correct choice is
Compare your answer with the correct one above