Question

If the diagonals of a rhombus measure 4 cm and 6 cm respectively, its area is –

i) 62

ii) 8 2

iii) 24 2

iv) 12 2​

Answer 1

$\bf \pink{Given}\begin{cases}&\sf{Measure\:of\:the\:First\:diagonal\:is\:\bf{4\:cm.}} \\ \\ &\sf{Measure\:of\:the\:Second\:diagonal\:is\:\bf{6\:cm.}}\end{cases}$

To FinD:-

The area of the rhombus.

Solution:-

We know that,

$\normalsize{\pink{\underline{\boxed{\bf{Area_{(rhombus)}=\dfrac{1}{2}\times\:d_{1}\times\:d_{2}}}}}}$

where,

• d1 is the first diagonal = 4 cm
• d2 is the second diagonal = 6 cm

Putting the values,

$\normalsize\implies{\sf{Area_{(rhombus)}=\dfrac{1}{2}\times4\times6}}$

$\normalsize\implies{\sf{Area_{(rhombus)}=\dfrac{1}{\cancel{2}}\times\cancel{4}\times6}}$

$\normalsize\implies{\sf{Area_{(rhombus)}=1\times2\times6}}$

$\normalsize\therefore\boxed{\mathfrak{\pink{Area_{(rhombus)}=12\:cm^2.}}}$

Area of the rhombus is 12 cm².

Your answer is option (iv).