SAT Math Multiple Choice Practice Question 443: Answer and Explanation

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Question: 443

5.

Note: Figure not drawn to scale.

In parallelogram ABCD above, AC = 3 and AD = 5. What is the area of ABCD ?

A. 12
B. 15
C. 18
D. 20
E. It cannot be determined from the information given.

Correct Answer: A

Explanation:

A The trick is to notice that this parallelogram is actually made of two equal triangles. By finding the area of the triangles, you can find the area of the parallelogram. The triangles are both right triangles, and the two sides given in the figure follow the 3:4:5 pattern. If you look at triangle ACD with as the base, the base is 3 and the height is 4. Now use the formula for area of a triangle:

That means the parallelogram is 2 × 6 = 12.

Also, if you estimate the area, the base is 5 and the height is less than 3, so the area is less than 15. The only answer less than 15 is A!

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