Question

If the side of a rhombus is 6 cm and its one diagonal is 10 cm, then find the area of the rhombus.

• A. $5\sqrt{7}{\text{cm}}^2$
• B. $10\sqrt{7}{\text{cm}}^2$
• C. $7\sqrt{5}{\text{cm}}^2$
• D. $15\sqrt{7}{\text{cm}}^2$

Answer 1

The correct option is B $10\sqrt{7}{\text{cm}}^2$

Side of the rhombus = 6 cm

Length of a diagonal = 10 cm

Semi-perimeter (s) of the triangle containing the diagonal,
$s=\frac{(6+6+10)}{2}$ = 11 cm

The area (A) of the triangle with sides a, b and c can be calculated using Heron's formula, given by:
$A=\sqrt{s(s-a)(s-b)(s-c)}$.

$=\sqrt{11(11-6)(11-6)(11-10)}$

$=\sqrt{11\times 5\times 5\times 1}$

$=\sqrt{275}$

$=\sqrt{25\times 7}$

$=5\sqrt{7}{\text{cm}}^2$

Therefore , area of the triangle containing the diagonal is $5\sqrt{7}{\text{cm}}^2$.

Area of rhombus
$=2\times \left(\text{Area of the triangle containing the diagonal}\right)$$=2\times \left(5\sqrt{7}\right)$
$=10\sqrt{7}{\text{cm}}^2$