Question

If the side of a rhombus is 6 cm and its one diagonal is 8 cm. Find the area of the rhombus in $c{m}^2$.

Answer 1

Side of the rhombus = 6 cm
One of the diagonal = 8 cm
Semi perimeter of the triangle containing the diagonal = $\frac{6+6+8}{2}=10cm$
Area of the triangle containing the diagonal =$\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{10(10-6)(10-6)(10-8)}=\sqrt{10\times 4\times 4\times 2}=8\sqrt{5}c{m}^2$
Area of rhombus = 2 (Area of the triangle containning the diagonal)
Area of the rhombus = 2 $\times 8\sqrt{5}c{m}^2=16\sqrt{5}c{m}^2$