Question

Find the area and perimeter of a rhombus with a diagonals 15 in and 20 in

Answer 1

Given data:

The diagonals of rhombus d1 = 15 in and d2 = 20 in

The area of the rhombus,

`\begin{gathered} A=(1)/(2)* d1* d2 \\ A=(1)/(2)*15*20 \\ A=150\text{ inches sq.} \end{gathered}`

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

`\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}`

The perimeter of the rhombus is,

`\begin{gathered} P=4* side \\ P=4*12.5 \\ P=50\text{ inches} \end{gathered}`

Thus, the area is 150 in. sq. and perimeter is 50 in.