Question

What is the area of a rhombus on which one side measures 10 cm and the diagonal measures 12 cm?

Answer 1

Rhombus $ABCD$

$AB=10cm$

$BC=10cm$

all sides of rhombus are equal.

Diagonal $AC=12cm$

So area of (tri $ABC$) by herini formula.

$=\sqrt{s(s-a)(s-b)(s-c)}$ , $s$ is semi perimeter & $a,b,c$ sides of triangles

$s-\frac{32}{2}=16cm$

Area $=\sqrt{16(16-10)(16-10)(16-12)}$

Area $=\sqrt{16\times 6\times 6\times 4}$

Area $=48{cm}^2$

Area (Rhombus $ABCD$) $=48\times 2=96$ ${cm}^2$.