Question

Find the area of the rectangle.

Short answer

The area of the given rectangle is $36\sqrt{5}$.

Step-by-step solution

Step 1. Write the formula for the area of the rectangle.

The area (A) of the rectangle is given by:

$A=L\times B$

Where L and B are the length and breadth of the rectangle.

Step 2. Find the area of the given rectangle.

The given diagram of the rectangle is:

From the given diagram, it can be noticed that the length of the given rectangle is $6\sqrt{10}$and breadth of the given rectangle is $3\sqrt{2}$.

Therefore, the values of L and B are$6\sqrt{10}$ and$3\sqrt{2}$ respectively.

Substitute the values of L and B in the equation $A=L\times B$to find the area of the rectangle.

$$\begin{gathered} A=L\times B \\ =6\sqrt{10}\times 3\sqrt{2} \\ =6\times 3\times \sqrt{10}\times \sqrt{2} \\ =18\times \sqrt{10\times 2} \\ =18\times \sqrt{20} \\ =18\times \sqrt{5\times 2^2} \\ =18\times 2\times \sqrt{5} \\ =36\sqrt{5} \end{gathered}$$

Step 3. Conclusion.

Therefore, the area of the given rectangle is $36\sqrt{5}$.