SAT Math Multiple Choice Practice Question 488: Answer and Explanation

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Question: 488


What is the area of quadrilateral ABCD in the figure above?

A. 50
C. 70
E. 75

Correct Answer: D


D Draw a line straight up from D to divide the shape into a rectangle and a triangle. The area of a 5-by-10 rectangle is 50. To get the area of the triangle, find the length of the base; you already know the height is 5. Use the Pythagorean theorem, or to save time, recognize that this is a 30°-60°-90° triangle because the hypotenuse is twice as long as the shortest side. The base is therefore 5. The area of the triangle is therefore . The total area of ABCD is therefore 50 + 12.5.

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