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The perimeter of a rhombus ABCD is $40$ cm. Find the area of a rhombus if it’s diagonal BD measures $12$ cm.

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106

answer is C.

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Detailed Solution

Given data:
Diagonal BD of rhombus =

12

cm
Perimeter of rhombus ABCD =

40

cm
We are aware that the perimeter is equal to the total of the lengths of all the rhombus sides, or 4s, where s is a rhombus side.
Using the method above, we can determine the side of the rhombus and obtain

40 = 4 s

s = 10

Now,
Create four right-angled triangles out of the rhombus.
So that each triangle has a

10

cm hypotenuse.

\frac{12}{2} = 6

cm
Utilizing Pythagorus' Theorem

= \sqrt{10^{2}} - 6^{2}

= 8

cm
Here,

8 + 8 = 16

cm [Measure of

d_{1}

equals the sum of the bases of two triangles]
Area of rhombus =

\frac{1}{2} \times d_{1} \times d_{2}

= \frac{1}{2} \times 16 \times 12

= 96 {cm}^{2}

Therefore, the area of the rhombus is

96 {cm}^{2}

, and the diagonal AC is

16

cm.

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