Question

Find the area of the figure. Use trigonometry and draw a diagram.

Answer 1

Area = 72

Step-by-step explanation:

All the sides are equal and there is an interior angle of 90 degrees, so we can say that figure is a square.

Then, to know the area, we need to know the length of the sides.

Since we know that the diagonal is 12, we can calculate the length of the sides using the following equation:

`\begin{gathered} d=\sqrt[]{a^2+a^2} \\ d=\sqrt[]{2a^2} \\ d=\sqrt[]{2}\cdot\sqrt[]{a^2} \\ d=\sqrt[]{2}\cdot a \\ d=a\sqrt[]{2} \end{gathered}`

where d is diagonal and a is the side of the square. Replacing d by 12 and solving for a, we get:

`\begin{gathered} 12=a\sqrt[]{2} \\ \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \frac{12}{\sqrt[]{2}}=a \end{gathered}`

Then, the area of the figure is equal to:

`\begin{gathered} \text{Area}=a* a \\ \text{Area}=\frac{12}{\sqrt[]{2}}*\frac{12}{\sqrt[]{2}} \\ \text{Area}=\frac{12*12}{\sqrt[]{2}*\sqrt[]{2}}=(144)/(2)=72 \end{gathered}`

Therefore, the area is 72.