tag:blogger.com,1999:blog-5388729698923619298.comments2010-12-14T15:16:13.739-06:00Word ProblemsChip Burkitthttps://plus.google.com/107568484919232242606noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-5388729698923619298.post-43373352696436012452010-12-14T15:16:13.739-06:002010-12-14T15:16:13.739-06:00Like a square, a rhombus has four equal sides, but...Like a square, a rhombus has four equal sides, but unlike a square, its angles are not all the same. The area of a rhombus, like that of a parallelogram is given by A = bh, where b is the length of the base (in this case, any side), and h is the height from the base to the opposite side. Solving this problem requires knowing how to find the length of a side of the rhombus. The height, 4, is given along with a portion of the base that forms the leg of a right triangle. Knowing the two legs of a right triangle, you can determine the length of the hypotenuse (the longest side) by the Pythagorean formula. If a, b are legs of a right triangle and c is the hypotenuse, then the following relation is true: a^2 + b^2 = c^2. In this case, we know a = 3 and b = 4. Therefore c^2 = 3^2 + 4^2 = 9 + 16 = 25. The square of 5 is 25, so c = 5.<br />Having obtained the length of a side of the rhombus, we can now calculate the area. A = bh = 5 x 4 = 20.<br />Note: I used b to represent the length of the base of the rhombus in the formula for the area and also to represent a leg of the right triangle in the Pythagorean formula. In each case b has a different meaning and the meanings should not be confused.Chip Burkitthttp://www.blogger.com/profile/00817016103778281416noreply@blogger.comtag:blogger.com,1999:blog-5388729698923619298.post-66326342793231253192010-12-14T15:03:11.934-06:002010-12-14T15:03:11.934-06:00The circumference of a circle is given by C = 2πr,...The circumference of a circle is given by C = 2πr, where r is the radius and π represents the ratio of a circle's circumference to its diameter (i. e., π = C/(2r)), which is 3.1415926.... By the way, 3 1/7 is a good approximation of π, with an error of less than -0.04%.<br />The radius of the circle in the problem is 3, so C = 2 x π x 3 = 6 x π ≈ 18.85. Good job!Chip Burkitthttp://www.blogger.com/profile/00817016103778281416noreply@blogger.comtag:blogger.com,1999:blog-5388729698923619298.post-79401592908295738192010-12-09T09:35:24.364-06:002010-12-09T09:35:24.364-06:0020 units squared20 units squaredsproutingflowershttp://sproutingflowers.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5388729698923619298.post-72026995603768887292010-12-09T09:17:43.635-06:002010-12-09T09:17:43.635-06:00This is the sort of problem I've encountered i...This is the sort of problem I've encountered in real life as a mom and crafter.<br /><br />18.85 unitssproutingflowershttp://sproutingflowers.wordpress.com/noreply@blogger.com