Question

A rhombus with diagonals 15 in and 20 in

Answer 1

Given data:

Diagonals if rhombus 15 inches and 20 inches.

Area of rhombus is,

$A=\frac{1}{2}\times d1\times d2$$\begin{gathered} A=\frac{1}{2}\times15\times20 \\ A=150\text{inches sq} \end{gathered}$

Now, to find the perimeter first find the side of the the rhombus

Diagonal is considered as diameter so radius will be the half of the diameter,

d1 = r1 = 7.5

d2 = r2 = 10

Finding the side by the pythagorean theorem,

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

Therefore, the perimeter of the rhombus is

$\begin{gathered} P=4h \\ P=4\times12.5 \\ P=50\text{inches} \end{gathered}$

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