ISEE Middle Level Quantitative : How to find the area of a trapezoid

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

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Example Questions

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

Square c

Note: Figure NOT drawn to scale

The above figure shows Square \(\displaystyle SQUA\)

\(\displaystyle SX = UY + 1\)

Which is the greater quantity?

(a) The area of Trapezoid \(\displaystyle SXYA\)

(b) The area of Trapezoid \(\displaystyle XQUY\)

Possible Answers:

(a) is the greater quantity

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

(a) and (b) are equal

(b) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

The easiest way to answer the question is to locate \(\displaystyle Z\) on \(\displaystyle \overline{SQ}\) such that \(\displaystyle SZ = UY\):

Square c

Trapezoids \(\displaystyle SZYA\) and \(\displaystyle ZQUY\) have the same height, which is \(\displaystyle SA = QU\). Their bases, by construction, have the same lengths - \(\displaystyle AY = ZQ\) and \(\displaystyle SZ = YU\). Therefore, Trapezoids \(\displaystyle SZYA\) and \(\displaystyle ZQUY\) have the same area.

Since \(\displaystyle SX = UY + 1\), it follows that \(\displaystyle SX = SZ+ 1\), and \(\displaystyle SX > SZ\). It follows that Trapezoid \(\displaystyle SXYA\) is greater in area than Trapezoids \(\displaystyle SZYA\) and \(\displaystyle ZQUY\), and Trapezoid \(\displaystyle XQUY\) is less in area.

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