In the figure below, cm. If is the image of by a rotation around with an angle of , find the area of approximating the result to the nearest hundredth.
Step 1: Find the length of .
Use Pythagoras' theorem, and solve for the length of .
Step 2: Find the area of .
The side lengths of a rotated image are the same as the corresponding side lengths of the original figure. Therefore,
Then, use the formula for the area of a triangle.
Step 3: Find the area of .
Use as the base and as the corresponding height.
The base length and the corresponding height are the same as . Therefore, the two triangles are equal in area.
Step 4: Find the area of .