1. The diameter of the smaller circle is 10 cm, so its radius is 5 cm (half of the diameter).
2. The diameter of the larger circle is 16 cm, so its radius is 8 cm (half of the diameter).
3. The two circles are touching externally at point T, which means that the sum of the radii of the two circles is equal to the distance between the centers of the two circles. Let's call this distance "d". Then:
d = 5 cm + 8 cm
d = 13 cm
4. The rectangle has a length of 18 cm and a width of x cm. Since the two circles are fitted into the rectangle, the width of the rectangle (x) must be equal to the sum of the radii of the two circles (d). Therefore:
x = 13 cm
5. Finally, we can find the area of the rectangle by multiplying its length and width:
Area = Length × Width
= 18 cm × 13 cm
= 234 cm²
So, the area of the rectangle is 234 square centimeters.
