Ineed with 10/38 part a., because it's the part which i don't understand. my only confusion is that (perhaps it's because i'm very tired at the moment and not thinking clearly) but i know to get either perimeter or area of the triangle i'd need two sides, however i only have one and i can't see any clues as to how to figure out the other side. any is appreciated, and any willing to show the step-by-step progress would also be very much appreciated and .

- kathryn

(20 pts)

A. is a trapezoid.  The area formula for a trapezoid is A = 1/2 h (base 1 + base 2).  Your bases are 7 and 17, so add those to get 24.  Now multiply 24 by the height, which is shown to be 6 (6 * 24 = 144), and then divide that in half (144/2 = 72.  That's the area.  The perimeter is a little tricky because you don't have the hypotenuse of the other triangle, but you can figure it out.  If you draw a straight line down from the top right where 7 meets the 10, that is a height of 6 also.  Now what you have, in essence, is 3 shapes: 2 right triangles and one square.  The side measures of the square are 7.  When you draw the height for the right triangle on the right side, you've created a situation where you have the hypotenuse and one leg.  Use Pythagorean's Theorem to find the base leg.  10^2 - 6^2 = b^2, 100-36=b^2, 64=b^2, and b=8. Now you have the base there of 8 and the base of the square as 7. Add those together and you get 15.  Well, you know the whole base is 17, so the base of the other right triangle has to be 2.  Now use Pythagorean's Theorem again to find the hypotenuse, which is the missing side.  6^2+2^2=c^2, 36+4=c^2, 40=c^2, and c=sqrt40, or 2*sqrt10, or 6.32455532