Rhombus: Area

AC = 12
BD = 7

So the diagonals are 7 and 12.

So A = [1/2]⋅7⋅12.

Cancel the denominator 2
and reduce 12 to, 12/2, 6.

7⋅6 = 42

So the area of the given rhombus is 42.

Recall that
for a rhombus,
the diagonals perpendicularly bisect each other.

Rhombus: Property

So the right side of the horizontal diagonal is,
the same as the left side,
4.

See this right triangle.

The sides are (height, 4, 5).
So this right triangle is
a (3, 4, 5) right triangle.

Pythagorean Triple

So the height is 3.

The vertical diagonal is bisected
by the other diagonal.

So the upper side of the vertical diagonal is,
the same as the lower side,
3.

The horizontal diagonal is, 4 + 4, 8.
The vertical diagonal is, 3 + 3, 6.

So A = [1/2]⋅8⋅6.

[1/2]⋅8 = 4

4⋅6 = 24

So the area of the given rhombus is 24.