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SAT Math Multiple Choice Practice Question 204: Answer and Explanation

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Question: 204

6.

The preceding figure is formed by attaching two equilateral triangles to a square with a side length of 4. What is the area of the figure?

A. 16
B. 24
C.
D.
E.

Correct Answer: D

Explanation:

D. All the lines in the drawing must be 4 units long. You know this fact because the square's sides all have a length of 4, so the side of the equilateral triangle touching the square is 4 units long. Because the triangles are equilateral, all sides are the same length. The area of the square is 4 × 4 = 16 square units. The equilateral triangles have 30°-60°-90° triangles inside of them; you can use your knowledge of special triangles to determine the area of these triangles.

Now you can see that the "height" of this triangle is , so the area of the triangle is . You have two of these triangles in the figure, so the area of the entire figure is the area of the square plus twice the area of each triangle =

.

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