Question 1083151
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<pre>
Draw the diagonal of the rhombus.


The diagonals divide the rhombus in four right-angled congruent triangles 

    (since the diagonals of the rhombus bisect each other and are perpendicular).

Each small right-angled triangle has the hypotenuse of 10 cm and one leg of {{{12/2}}} = 6 cm.

Hence, the second leg of each small right angled triangle is {{{sqrt(10^2-6^2)}}} = {{{sqrt(100-36)}}} = {{{sqrt(64)}}} = 8 cm.


Then the area of each small right-angled triangle  is {{{(1/2)*6*8}}} = 24 cm^2.


Thus the area of the rhombus is 4*24 = 96 cm^2.


Then the height of the rhombus = {{{96/10}}} = 9.6 cm.
</pre>

Solved.



On properties of rhombis, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-are-perpendicular.lesson>Diagonals of a rhombus are perpendicular</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-bisect-its-angles.lesson>Diagonals of a rhombus bisect its angles</A>

in this site.



Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part if this textbook under the topic "<U>Properties of rhombis</U>".