Question

8. The rhombus given in Fig. 14.33 has
been transformed to a rectangle by
rearranging the shaded parts of the
rhombus as shown. Find the
a) length of the rectangle.
b) breadth of the rectangle.
c) area of the rectangle.
d) area of the rhombus.
​

Answer 1

${\huge{\underline{\sf {\orange{Answer}}}}}$

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a. 12 cm

b. 4 cm

c. 48 ${cm}^{2}$

d. 48 ${cm}^{2}$

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${\huge{\underline{\sf{\orange{Explanation :}}}}}$

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Given :

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Lengths of the diagonals of a rhombus = 8cm , 12cm

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To find :

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• Length of the rectangle formed

• Breadth of the rectangle formed

• Area of the rectangle formed

• Area of the rhombus

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Solution :

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We know that the diagonals of the rhombus bisect each other.

So, half of the diagonals = 4cm , 6cm

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The rectangle has the same length as the diagonal (12 cm) of the rhombus = 12 cm

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The rectangle formed has the same height as the half of the diagonal (8 cm) = 4cm

So, the Breadth of the rectangle = 4 cm

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Area of the rectangle = ( Length × Breadth )

Area = ( 12 × 4 ) ${cm}^{2}$

Area = 48 ${cm}^{2}$

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Area of the rhombus =

$\sf \frac{1}{2} \times (product \: of \: digonals)$

$\sf \frac{1}{2} \times (12 \times 8) \: {cm}^{2}$

$(\sf\frac{1}{2 } \times 96) \: {cm}^{2}$

$\sf\: 48 \: {cm}^{2}$

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Note :

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The product of both the rectangle and rhombus are same because the area of the paper ( or anything ) used is of the same area. The size of the paper did not change , i.e. , no extra paper was used or no paper was left to make the rectangle so, the area remained the same.

Answer 2

Answer:

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