The area of a rhombus is half the product of the lengths of its diagonals.
288 in^2
Practice makes perfect
The area of a rhombus is half the product of the lengths of its diagonals. Therefore, to find the area we will first find the lengths of the diagonals. The diagonals of a rhombus are perpendicular and they bisect each other.
The indicated lengths are from the vertices to the center. Since the diagonals bisect each other we know that the other half of each diagonal must have the same length.
To find the lengths of diagonals we will use the Segment Addition Postulate.
d_1: 12+12=24 inches
d_2: 12+12=24 inches
We can now find the area of the rhombus by substituting these values into the formula A= 12d_1 d_2. Let's do it!
A=1/2d_1 d_2
⇓
A=1/2(24)(24)=288in^2
