Wednesday, December 8, 2010

Rhombus Area

Find the area of the rhombus depicted above.

2 comments:

Anonymous said...

20 units squared

Chip Burkitt said...

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.
Having obtained the length of a side of the rhombus, we can now calculate the area. A = bh = 5 x 4 = 20.
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.