The perimeter of a rhombus is 50 cm and its one of the diagonal is 12 cm then find the - Maths - Mensuration

Question

The perimeter of a rhombus is 50 cm and its one of the diagonal
is 12 cm then find the area of rhombus

Gursheen kaur. · Accepted Answer

Perimeter = 4*side

50=4*side

50/4= side

side = 12.5 cm

where , side of a rhombus = $\sqrt{{(\frac{d_{1}}{2})}^{2} + {(\frac{d_{2}}{2})}^{2}}$

$12.5 = \sqrt{{(\frac{12}{2})}^{2} + {(\frac{d_{2}}{2})}^{2}} 12.5 = \sqrt{36 + {(\frac{d_{2}}{2})}^{2}} s q u a r i n g b o t h s i d e s, w e g e t, 156.25 = 36 + {(\frac{d_{2}}{2})}^{2} 156.25 - 36 = {(\frac{d_{2}}{2})}^{2} 120.25 = {(\frac{d_{2}}{2})}^{2} o r \frac{d_{2}}{2} = \sqrt{120.25} \frac{d_{2}}{2} = 10.9 d_{2} = 21.9 c m$

Area of a rhombus is $\frac{1}{2} � d_{1} � d_{2}$ .

$d_{1} = 12 c m a n d d_{2} = 21.9 c m$

Thus,

$A r e a = \frac{1}{2} * 12 * 21.9 = 131.4 {c m}^{2}$

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The perimeter of a rhombus is 50 cm and its one of the diagonal is 12 cm then find the area of rhombus .