Q: Sketch a trapezoid with the following measurements: left side of height b, right side of height a, and base of length a+b. Simply connect the tops of the left and right sides to complete the trapezoid. Divide the base of the triangle into lengths a and b so that two right triangles of lengths a, b, and c is formed. The third triangle will have two sides of length c and a hypotenuse of length d. The two smaller triangles are congruent (identical). The area of a trapezoid is: A = ½(b1 + b2)h where b1 is one straight side of the trapezoid, b2 is the other straight side of the trapezoid, and h is the height of the trapezoid. For this trapezoid: b1 is a, b2 is b, and h is a+b.  The area of this trapezoid is A = ½(a +b)(a+b) .  Expanding the binomial yields: A = ½(a2 + 2ab + b2). The area of a right triangle is: A = ½bh where b is the base of the triangle and h is the height. This trapezoid has been broken into three different triangles; therefore, the areas need to be added together. First, find the area of each one and then add all three together.  Because two of the triangles are identical, you can simply multiply the area of the first triangle by two: 2A1 = 2(½bh) = 2(½ab) = ab. The area of the third triangle is A2 = ½bh = ½c*c = ½c2. The total area of the trapezoid is A1 + A2 = ab + ½c2. Because both of these calculations are equal to the total area of the trapezoid, you can set them equal to each other. Once they’re set equal to each other, you can reduce the equation to its simplest form.   ½(a2 + 2ab + b2) = ab + ½c2. Multiply both sides by 2 to get rid of the ½: (a2 + 2ab + b2) = 2ab + c2. Subtract out the 2ab: a2 + b2 = c2. You’re left with the proof: a2 + b2 = c2.
A: Draw a trapezoid with base a+b and sides a and b. Divide the trapezoid into three right triangles, two of which are congruent. Calculate the area of the trapezoid using the area formula. Find the area by summing the areas of the three triangles. Set the different area calculations equal to each other.

Q: While you are deciding whether or not you want to get back together with your ex, you should not be in contact with them. It is important to have no contact with your ex to deal with your emotions, process the breakup, and prepare to move on. Even if you decide that you want to get back together, you will still need time to yourself and so will your ex. Before you try to determine if getting back together with your ex is the right decision, you may want to find out if your ex is even available. If it has been a while since the two of you broke up, then your ex may be seeing someone else. In this case, you may be better off pursuing relationships with other people instead. Don’t try to reunite with your ex if they are seeing someone else. Just pursue your own interests, see other people, and be patient. While the relationship may have been great, sometimes it really is better to let a relationship or former partner go. Before you start trying to get your ex back, consider your reasons for wanting to do so.  Some good reasons to get back together include: your timing was off the first time you were together, you needed more time to get over a previous relationship, or you have developed a new appreciation for what your ex provided for you.  Some bad reasons to try to get back with your ex include: you're scared of being alone (of course you're lonely after a relationship goes south, but that doesn't mean you should plunge right back into that relationship); you miss the familiar (again, there's no issue with this feeling, but it doesn't mean you should get back together); you're jealous of their new relationship (again, a totally allowable feeling, but not a good basis for a fresh relationship attempt). You should enlist a trusted friend, family member, or therapist, to consider why you want to get back with your ex. They will help you tease out some less-than-stellar reasons and maybe help you move on. In addition to considering your reasons for wanting to reunite with your ex, you should also consider the relationship overall to decide if it is worth reviving. If you broke up because the relationship was bad for one or both of you, then you may want to take some more time to consider whether it is worth reviving. For example, if you fought all of the time and did not enjoy spending time together, then the relationship is probably not worth reviving. If you have a lot of mixed feelings about why you want to get back together and if the relationship is worth reviving, try making a list of pros and cons to help you decide. Be honest with yourself as you make this list and don’t omit anything because it seems small or insignificant. List everything you can to get a good picture of the relationship and make a decision.
A: Keep your distance. Determine if your ex is available. Consider why you want your ex back. Decide if the relationship was healthy and worth reviving. Make a list of pros and cons if you are unsure.

Q: Purchase several ripe apples, then eat them or cut them until you reach their cores. Carefully remove the seeds from around the cores of the apples, being sure to pick out every seed before disposing of the cores.  Be aware that most apple trees grown by farmers and gardeners come from grafted trees, and are not planted directly from the seed. Planting trees from apple seeds produced highly variable fruit, since apple trees are not guaranteed to grow according to their type or variety. The more seeds you plant, the more likely it will be that one of the trees will produce edible apples, as opposed to less edible varieties like crab apples. There is about a one in ten success rates of seeds growing into apple trees that produce fruit good enough to eat. Try to start the process of preparing the seeds during the fall, so that by the beginning of spring, the seeds are ready for planting. After you extract the seeds from the apple or apples, add the seeds to a bowl of water. If they float, throw them away, because they are less likely to grow. Lay the other seeds out on a paper towel and allow them to dry for three to four weeks. Flip the seeds over every two days so that they dry evenly on both sides. After a couple days of drying, purchase some peat moss. Pour a few tablespoons of the peat moss on the paper towel, then sprinkle on a few drops of water. Use your hands to mix up the peat moss and seeds. After you mix up the seeds and peat moss, pour the mixture into a ziplock bag. Write the date on the bag with a marker, then place the bag in the refrigerator for three months.  The process of storing the seeds in moist, cold conditions is called stratification. Stratification softens the hard outer coat of the seed and encourages the embryo inside the seed to start germinating. After three months, remove them from the refrigerator, and allow them to warm up so that you can plant them.
A:
Remove apple seeds from the cores of several apples. Dry the seeds on a paper towel. Mix the seeds with peat moss. Put the seeds and peat moss in a bag and refrigerate.