Chapter 11.2, Problem 2CYP

To determine

To find: The area of the ear-ring.

Answer to Problem 2CYP

The area of the earring is $8.484{\text{cm}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

The Figure is in the shape of isosceles trapezoid.

The height of trapezoid is obtained as,

  $\begin{array}{l}{h}^2=3^2-\frac{{\left(4-2\right)}^2}{2}\\ h^2=9-1\\ h^2=8\\ h=\sqrt{8}\end{array}$

The area of the trapezoid is in the form,

  $A=\left(\frac{a+b}{2}\right)h$

Then,

  $\begin{array}{c}A=\left(\frac{4+2}{2}\right)\left(\sqrt{8}\right)\\ =\left(3\right)\left(\sqrt{8}\right)\\ =8.484{\text{cm}}^2\end{array}$