Question

How do we find the area of a rhombus ?

Answer 1

`A=1/2L_1L_2` where `L_1` and `L_2` are the diagonal lengths of the rhombus.

Explanation:

`A=1/2L_1L_2` where `L_1` and `L_2` are the diagonal lengths of the rhombus - The rhombus can be visualized as `2` congruent triangles with one of the diagonals being a shared side. Because each of a rhombus's diagonals perpendicularly bisect the other, the opposite bisector represents the height of the each triangle. The formula for area of a triangle is `1/2bh`, or in this case `1/2L_1(1/2L_2)`. Since there are 2 of these triangles in a rhombus, the equation for area of a rhombus is:
`2*1/2L_1(1/2L_2)`, which simplifies to:
`A=1/2L_1L_2`

Answer 2

As below.

Explanation:

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`color(maroon)("Case 1 : Known diagonals :-"`
`"Area of Rhombus " = A = (1/2) * d_1 * d_2, " where " d_1, d_2 " are the diagonals"`

`color(maroon)("Case 2 : Known side and interior angle :-"`
`"Area of Rhombus " = A = a^2 sin theta, " where 'a' is the side and "theta " the interior angle of the rhombus"`

`color(maroon)("Case 3 : Known side and height :-"`
`"Area of Rhombus " = A = a * h " where 'a' is the side and 'h' the height of the rhombus"`