<p>On one of the official practice tests from the CB (it's the online 2008 version linked in the Silverturtle guide), there's a question about the perimeter of a trapezoid.</p>
<p>It gives you a picture of a trapezoid, with a side 17 on the left, 15 on the right, and a side 20 on the top. The missing side is across from the top side of the trapezoid. </p>
<p>How are you supposed to solve this? Is there a specific rule for trapezoids, or are you supposed to use right triangles to figure it out? </p>
<p>I had no idea the SAT tested obscure shapes like trapezoids and am freaking out haha.</p>
<p>Hey there. :)</p>
<p>Trapezoids have one pair of parallel sides.</p>
<p>See how on the right side there are two right angles? So pretty much, it is a composite figure- a rectangle and a triangle. So, you could view the bottom side as the rectangle’s bottom and the triangle’s bottom. The rectangle’s bottom would be 20, because rectangles have two parallel side/the parallel sides are the same length.</p>
<p>You can use the Pythagorean Theorem in order to solve for the missing length of the triangle. 17^2=15^2+x^2. Solve, and x=8. 8+20=28. For the total perimeter of the trapezoid, 28+20+15+17= 75, C.</p>
<p>I hope my logic makes sense for you.</p>
<p>I understand the part about using the Pythagorean Theorem, but I’m not sure how you were able to get the values that you did.</p>
<p>For example, I choose the left side (17):</p>
<p>A^2 + B^2 = C^2</p>
<p>All I can fill in is “A^2”, because I don’t know the measurement of any of the other sides:</p>
<p>17^2 + B^2 = C^2</p>
<p>I’m guessing that the “15^2” is supposed to “B^2” and then “C^2” would be the value squared of the left and right sides of the inner rectangle?</p>
<p>17 would be the hypotenuse, while 15 would be one of the legs. Since there is a rectangle, you are able to know that parallel sides are equal. Gosh I need to draw a picture, but does that help? If it doesnt Ill try to use l’s and slashes to make a triangle. xD</p>
<p>No, it makes sense. 
I drew out a trapezoid onto a piece of paper and followed your instructions. Thank you for the help</p>
<p>Thanks a ton apples! After your explanation I was able to see that it’s basically a rectangle with an awkward little abscess coming out of it, can’t believe I didn’t realize drawing the altitude cut off the little thing and that it was equal to 15.</p>
<p>I understand how you draw two altitude to make a rectangle in the middle while two triangles on the side, but how do you know two smaller triangles will form a right triangle?</p>
<p>@Dusterbug: Im really glad I could help!</p>
<p>@forthesakeofedu: Two triangles? The way I was meaning to explaining, there are two shapes in the composite figure: one rectangle and a triangle. The triangle is a right triangle since a rectangle has four right angles, and when you draw the imaginary line dividing the triangle and the rectangle, the line hits perpendicular to the bottom side, thus creating a right angle on the triangle.</p>
<p>In that case. The side with 15 has to be perpendicular to the base…</p>