Question

if the measure of an angle is 60degree and the perimeter of a rhombus is 48cm, then find the area of the rhombus
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Answer 1

Answer:

cm²

Step-by-step explanation:

Let ABCD be a RHOMBUS.

Let ∠ABC be 60°

Given, perimeter of rhombus is 48 cm.

We know that all the 4 sides of a rhombus are equal.

∴ Side of the rhombus = 48÷4

                                    = 12 cm

∠ABC = 60° ; We know that in ΔABC, AB=BC   [∵ They are sides of a rhombus]

∴ ∠BAC = ∠BCA = (180°-60°)÷2

                           = 60°

∴ ∠BAC = ∠BCA = 60°

∴ We come to know that ΔABC is an EQUILATERAL TRIANGLE.

⇒ Area of ΔABC =  

⇒ Area =  

⇒ Area =  cm²

⇒ ∴ Area of rhombus ABCD = 2×Area of ΔABC

                                              = 2×

                                              =  cm²

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