Given data:
The diagonals of rhombus d1 = 15 in and d2 = 20 in
The area of the rhombus,
[tex]\begin{gathered} A=\frac{1}{2}\times d1\times d2 \\ A=\frac{1}{2}\times15\times20 \\ A=150\text{ inches sq.} \end{gathered}[/tex]Now, to find the perimeter of rhombus we first find the side of rhombus.
The diagonal of the rhombus is considered as diameter, so the radius will be
d1 = r1 = 7.5
d2 = r2 = 10
So, by using the pythagorean theorem we find the side of the rhombus
[tex]\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}[/tex]The perimeter of the rhombus is,
[tex]\begin{gathered} P=4\times side \\ P=4\times12.5 \\ P=50\text{ inches} \end{gathered}[/tex]Thus, the area is 150 in. sq. and perimeter is 50 in.
