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Lesson: Challenging Problem Solving - 31t01

Advanced Geometry: Multiple Figures

[Page 31 of 37]

Review the following problem and then proceed to the task below.


In the figure above, RSTU is a square with an area of 8 and JKL is an isosceles triangle. If JS = UL = 2, then what is the perimeter of the shaded figure?

Consider your answers to the following questions, and then click Continue.
  1. What is the question asking us to find?
  2. What information has it provided to us?
  3. What shared feature will get us to the correct answer?

  1. What is the question asking us to find?
    • The perimeter of the shaded region that consists of: two sides of the square (ST and TU), the legs of the large triangle (JK and KL), and the lengths JS and UL.
  2. What information has it provided to us?
    • The area of the square is 8, and the length of JS and UL is 2.
  3. What shared feature will get us to the correct answer?
    • We're given concrete information concerning square RSTU, but we need to find out more information about the larger triangle (specifically, its legs). The two figures share segment SU, but they also share small triangle STU.
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