(Continued from above)Properties and important points to remember-
• Rhombus is a special type of parallelogram, where all the four sides are the same length. It, however, has all the properties of a parallelogram.
• The diagonals of a rhombus always bisect each other at right angles i.e. form 90 at the point of intersection.
• The area of a rhombus equals to: (base * altitude). Other method could be to use length of diagonals i.e. 1 /2 times product of diagonals. Say
d1 and d2 is the length of respective diagonal. Then area A = 1/2(d1 * d2).
Example6 : Given- find the area of the rhombus, whose perimeter is 120 feet and one of its diagonal has a length of 40 feet.
Step 1: The perimeter is 120 ft (Given).
Step 2: To get sides of the rhombus divide by 4, which equals to 30 feet.
Step 3: You know that the length of the side OC of the right triangle is equal to half of the diagonal length i.e. it equals 20 ft.
Step 4: Now in right BOC, length of side BO can be calculated using Pythagorean Theorem i.e.202 + BO2 =302
Thus BO2 = (302 - 202).
It gives BO = 22.4 feet (rounded)
Step 5: Area the rhombus equals to 4 times the area of
BOC i.e.
4 * [1/2*(22.4 x 20)].
Thus area of rhombus is 896 ft2, as the final answer.
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BOC, length of side BO can be calculated using Pythagorean Theorem i.e.