Question

Find the missing values.

Diagonal - $1\left(d_1\right)$	Diagonal - $2\left(d_2\right)$	Area of rhombus
$12cm$	$16cm$
$27mm$		$2025m{m}^2$
$24m$	$57.6m$

• A. $96c{m}^2;150mm;691.2m^2$.
• B. $96c{m}^2;50mm;691.2m^2$.
• C. $96c{m}^2;150mm;91.2m^2$.
• D. None of these

Answer 1

The correct option is A $96c{m}^2;150mm;691.2m^2$.

If two diagonals of a rhombus is given then the area is given by,

$\frac{1}{2}\times \text{diagonal 1}\times \text{diagonal 2}$

for 1st row,

diagonal 1 = 12 cm

diagonal 2 = 16 cm

$\therefore \text{area}=\frac{1}{2}\times 12\times 16=96c{m}^2$

for 2nd row,

diagonal 1 = 27 mm

diagonal 2 = x mm (say)

area $=2025m{m}^2$

$\therefore$ By the formula we have,

$\frac{1}{2}\times 27\times x=2025\Rightarrow x=\frac{2025\times 2}{27}=150mm$

for 3rd row,

diagonal 1 = 24 m

diagonal 2 = 57.6 m

$\therefore \text{area}=\frac{1}{2}\times 24\times 57.6=691.2m^2$

$\therefore$ option A is correct.