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Question

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


Solution

Rhombus $$ABCD$$
$$AB=10cm$$
$$BC=10cm$$
all sides of rhombus are equal.
Diagonal $$AC=12cm$$
So area of (tri $$ABC$$) by herini formula.
$$=\sqrt { s\left( s-a \right) \left( s-b \right) \left( s-c \right)  } $$ ,  $$s$$ is semi perimeter & $$a,b,c$$ sides of triangles
$$s-\dfrac { 32 }{ 2 } =16cm$$
Area $$=\sqrt { 16\left( 16-10 \right) \left( 16-10 \right) \left( 16-12 \right)  } $$
Area $$=\sqrt { 16\times 6\times 6\times 4 } $$
Area $$=48{ cm }^{ 2 }$$
Area (Rhombus $$ABCD$$) $$=48\times 2=96$$ $${ cm }^{ 2 }$$.

Mathematics

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