Question

1. Find area of a rhombus in which one side is equal to 15cm, and one of whose diagonal 24cm.​

Answer 1

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OA = $\frac{1}{2}$(AC) = $\frac{1}{2}$ (24) = 12 cm and AB = 15

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$(AB)^2 = (OA)^2 + (OB)^2$

$(15)^2 = (12)^2 + (OB)^2$

$(OB)^2= (15)^2– (12)^2$

$(OB)^2 = 225 – 144 = 81$

$(OB)^2 = (9)^2$

$OB = 9 cm$

$BD = 2 × OB$

$= 2 × 9$

$= 18 cm$

Hence, Area of the rhombus ABCD = ($\frac{1}{2}$ x AC x BD)

= ($\frac{1}{2}$x 24 x 18)

$= 216^2$