Question

1.The diagonals of a rhombus are 4 cm and 6 cm. Find its area and perimeter.

Book Back answer is:-
Area =12 cm²
Perimeter = 4√13 cm.




Read the questions by step by step explanation.
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Answer 1

Answer:

area =  12cm^2

Step-by-step explanation:

area = pq/2

=4cm*6cm/2

= 24cm^2/2

= 12cm^2

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Answer 2

$\huge\sf\pink{Answer}$

☞ Area is 12 cm² & Perimeter is 4√13 cm

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$\huge\sf\blue{Given}$

✭ Diagonals of a Rhombus are 4 cm & 6 cm

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$\huge\sf\gray{To \:Find}$

◈ The Area and perimeter?

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$\huge\sf\purple{Steps}$

Area of a Rhombus are given by,

$\underline{\boxed{\sf Area_{Rhombus} = \dfrac{d_1 \times d_2}{2}}}$

Substituting the given values,

➝ $\sf Area_{Rhombus} = \dfrac{d_1 \times d_2}{2}$

➝ $\sf Area = \dfrac{6\times 4}{2}$

➝ $\sf Area = \dfrac{24}{2}$

➝ $\sf \red{Area = 12 \ cm^2}$

Before finding the perimeter let's find the length of the side of the Rhombus,

$\underline{\boxed{\sf a = \sqrt{(\dfrac{d_2}{2})^2+(\dfrac{d_1}{2})^2}}}$

Substituting the given values,

➳ $\sf a = \sqrt{(\dfrac{d_1}{2})^2+(\dfrac{d_2}{2})^2}$

➳ $\sf a = \sqrt{(\dfrac{6}{2})^2 + (\dfrac{4}{2})^2}$

➳ $\sf a = \sqrt{3^2+2^2}$

➳ $\sf a = \sqrt{9+4}$

➳ $\sf a = \sqrt{13}$

Perimeter of a Rhombus is given by,

$\underline{\boxed{\sf Perimeter_{Rhombus} = 4a}}$

Substituting the values,

»» $\sf Perimeter_{Rhombus} = 4a$

»» $\sf Perimeter = 4\times \sqrt{13}$

»» $\sf \orange{Perimeter = 4\sqrt{13}}$

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