ISEE Mathematics Achievement Question 284: Answer and Explanation

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Question: 284

14.

ABC is an equilateral triangle. What is the perimeter of this figure?

  • A. 4 + 2π
  • B. 4 + 4π
  • C. 8 + 2π
  • D. 8 + 4π

Correct Answer: C

Explanation:

C The question states that triangle ABC is equilateral, so all 3 sides are equal to 4. Label AC as 4 and BC as 4. The question asks for perimeter, not area. So, there are two sides of the triangle that are part of the perimeter, so add them together: AB + BC = 4 + 4 = 8. Eliminate (A) and (B) since the choice must have an 8 in it. Now, find the rounded portion. The rounded portion is half of the circumference (i.e., a semicircle). Since you labeled BC as 4, you should see that the diameter of the circle must also be 4. If C = πd, then half of the circumference is πd. Plug in the value for the diameter and simplify: π(4) = 2π. The full expression for the perimeter will then read 8 + 2π. The correct answer is (C).

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