The lengths of the horizontal and vertical sides are easily determined. The slant side is seen to be the hypotenuse of a 3-4-5 triangle (times 2), so is 10 units long. The perimeter is the sum of the side lengths:

5 + 8 + 11 + 10 = 34

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You can always estimate the length of the hypotenuse of a right triangle as being between 1 and 1.5 times the length of the <em>longest</em> side. Here, the longest side of the right triangle whose hypotenuse is of interest is 8 units, so the hypotenuse will be between 8 and 12 units long. That means the perimeter of the blue trapezoid will be between 32 and 36, a guess of sufficient accuracy to allow you to choose the correct answer.

In a figure like this, you can also measure the hypotenuse on the grid. Using a compass, ruler, or a piece of paper with a couple of marks, you can rotate the slant length so that it corresponds to a vertical or horizontal grid line. Then the length of it is easily estimated to good accuracy. (See the second attachment.) As we said in the previous paragraph, even poor accuracy is sufficient to choose the correct answer.

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3 years ago