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Some of the rhombus' properties: a) The sides of a rhombus are all congruent. (the same length). b) The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half. Now back to our question : Given that the two diagonals are #30, and 16#, From Pythagorean theorem, we know SInce
#AB=BC=CD=DA#, Download PDF Formulas of Rhombus
Wondering how to find the perimeter of a rhombus? Just like any polygon, the perimeter of the rhombus is the total distance around the outside, which can be simply calculated by adding up the length of each side. In the case of a rhombus, all four sides are of similar length, thus the perimeter is four times the length of aside. Or as a formula: Perimeter of rhombus = 4 a = 4 × side. Here, ‘a’ represents each side of a rhombus. About the Perimeter of Rhombus FormulaA rhombus is a 2-dimensional (2D) geometrical figure which consists of four equal sides. Rhombus has all sides equal and its opposite angles are equivalent in measurement. Let us now talk about the rhombus formula i.e. area and perimeter of the rhombus. The Perimeter of a RhombusThe perimeter is the sum of the length of all 4 sides. In the rhombus all sides are equal. Thus, the Perimeter of rhombus = 4 × side So, P = 4s In which, S = length of a side of a rhombus Area of Rhombus FormulaThe area of a rhombus is the number of square units in the interior of the polygon. The area of a rhombus can be identified in 2 ways: i) Multiplying the base and height as rhombus is a unique kind of parallelogram. Area of rhombus = b × h In which, B = base of the rhombus H = height of the rhombus ii) By determining the product of the diagonal and dividing the product by 2. Area of rhombus formula = \[\frac {1}{2}\] × d1 × d2 In which, d1 × d2 =diagonal of the rhombus Derivation of Area of RhombusLet MNOP is a rhombus whose base MN = b, PN ⊥ MO, PN is a diagonal of rhombus = d1, MO is diagonal of rhombus = d2, and the altitude from O on MN is OZ, i.e., h.
= 2 × \[\frac {1}{2}\] MN × OP sq units. = 2 × \[\frac {1}{2}\] b × h sq. units = base × height sq. units
= 4 × \[\frac {1}{2}\] × MZ × ZN sq. units = 4 × \[\frac {1}{2}\] × d2 × \[\frac {1}{2}\] d1 sq. units Thus, = 4 × \[\frac {1}{8}\] d1 × d2 sq. units = \[\frac {1}{2}\] × d1 × d2 Hence, the area of a rhombus = \[\frac {1}{2}\] (product of diagonals) sq. units. Fun Facts
A rhombus has opposite angles equivalent to each other, while a rectangle has opposite sides equal. Finding the Perimeter of a Rhombus when only Diagonals are knownIn many questions, you will see that the length of the sides of the rhombus is not given. Instead, the question will provide you with the length of its diagonals. You can use the diagonals to find the side of the rhombus and calculate its perimeter. Here is how you can do it:
X2 = \[\frac {a} {2}^2 + \frac {b} {2}^2 \], which gives us, X2 = \[\frac {(a^2+b^2)} {4} \] X = \[\sqrt \frac {(a^2+b^2)} {2} \]
4 × \[\sqrt \frac {(a^2+b^2)} {2} \]
Solved Examples1. Evaluate the area of the rhombus MNOP having each side equal to 15 cm and one of its diagonals equal to 18 cm. Ans: Given:- MNOP is a rhombus in which MN = NO = OP = PM = 15 cm MO = 18 cm Thus, MZ = 9 cm In ∆ MZP, MP2 = MZ2 + ZP2 ⇒ 152 = 92 + ZP2 ⇒ 225 = 81 + ZP2 ⇒ 144 = ZP2 ⇒ ZP = 12 Hence, NP = 2 P = 2 × 12 = 24 cm Now, to find out the area of the rhombus, we will apply the formula i.e. = \[\frac {1}{2}\] × d1 × d2 = \[\frac {1}{2}\] × 18 × 24 = 216 cm2 2. Find the perimeter of a rhombus MNOP whose diagonals measure 20 cm and 24 cm respectively? Ans: Given: d1 = 20 cm d2 = 24 cm MZ= \[\frac {20}{2}\] = 10cm NZ= \[\frac {24}{20}\]= 12 cm ∠MZP = 90° Now applying the Pythagorean Theorem, we know that MN2= MZ2+ NZ2 MN = \[\sqrt {(100+144)} \] = 15.62 cm Since, MN = NO = OP = MP, Therefore, Perimeter of MNOP = 15.62 × 4 = 62.48 cm. Properties of a RhombusIdentifying a rhombus is not that difficult. There are some properties of a rhombus that will help you determine whether a given figure is a rhombus or not. If a shape meets the following conditions, then it is a rhombus:
Revising the Perimeter of Rhombus Formula - Explanation, Area, Solved Examples and FAQsThe Perimeter of Rhombus Formula is one of the most important formulas of Mathematics. It comes under mensuration, which is a crucial chapter of Maths. You must have a clear understanding of the Perimeter of Rhombus Formula - Explanation, Area, Solved Examples and FAQs to ensure a good score in your finals. Once you have a firm grasp of the perimeter and area of a rhombus, you will be able to solve any question related to this concept. That is why you should practice and revise the Perimeter of Rhombus Formula - Explanation, Area, Solved Examples and FAQs thoroughly. Here are some revision tips:
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