SAT Math : How to find the length of the side of a trapezoid

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #2 : Quadrilaterals

Square 1

The above figure shows Square is the midpoint of  is the midpoint of  is the midpoint of . Construct 

. Which of the following expresses the length of   in terms of ?

Possible Answers:

Correct answer:

Explanation:

Construct  as shown in the diagram below:

Square 1

Quadrilateral  is a rectangle, so opposite sides are congruent. Therefore, .

Since  is the midpoint of ,

Since  is the midpoint of 

.

 is a right triangle, so, by the Pythagorean Theorem, 

Substituting: 

Apply the Product of Radicals and Quotient of Radicals Rules:

 

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