SAT Math Multiple Choice Practice Question 215: Answer and Explanation
The preceding figure is constructed by appending equilateral triangles to three sides of a rectangle. If the rectangle is 6 inches long and 2 inches wide, what is the area of the figure, in square inches?
Correct Answer: C
C. Get the easy part out of the way first: Figure out the area of the rectangle. Area for rectangles is length × width, so the area is 6 × 2 = 12 square inches. Next, work on the biggest triangle. It's an equilateral triangle, so you can divide it in half and have two 30°-60°-90° triangles. You may recall that the side opposite the 60° angle is equal to times the side opposite the 30° angle. Because the base of the equilateral triangle is 6, the side opposite the 30° angle is half of that, or 3 inches, making the height of the triangle . The area of a triangle is , so in this case, . Determining the area of the smaller triangles is similar. Cut them up into 30°-60°-90° triangles. You can now determine that the height is ; therefore, the area of each little triangle is . You have two of these triangles, so their total area is . The area of the figure is the area of the rectangle plus the area of the big triangle plus the area of the small triangles, which equals , Choice (C).