To find the total surface area, add the areas of the two circles and the rectangle:

1. Area of the two circles: 56.52 cm²
2. Area of the rectangle: 150.72 cm²
   Total Surface Area = Area of the two circles + Area of the rectangle
   \[\text { Total Surface Area} = 56.52 \space \text { cm} ^ 2 + 150.72 \space \text { cm} ^ 2 = 207.24 \space \text { cm} ^ 2\]

Supplemental Knowledge

When calculating the total surface area of a composite shape, it’s essential to understand how to find the areas of individual shapes and then sum them up appropriately. Here are some key concepts:

1. Area of a Circle:
   • The formula for the area of a circle is \(\pi r^ 2\), where \(r\) is the radius.
   • Given that the combined area of two circles is 56.52 cm², each circle has an area of 28.26 cm².
2. Area of a Rectangle:
   • The formula for the area of a rectangle is \(\text { length} \times \text { width} \).
   • Given that the area of the rectangle is 150.72 cm², this value will be used directly in our calculations.
3. Total Surface Area:
   • To find the total surface area, sum up the areas of all individual shapes involved.
   • In this case, add the areas of both circles and the rectangle.

Theory in Practice

Imagine designing or building an artwork with circular and rectangular components; understanding how to calculate surface areas accurately will enable you to use materials more efficiently while attaining precise measurements for your project.
Assuming you were creating a decorative plaque with two circular engravings on a rectangular base, knowing how to calculate its area would allow you to accurately gauge how much paint or material would be necessary in order to complete its creation.

Mastering geometry can significantly enhance your problem-solving skills in real-world applications! At UpStudy, we provide advanced calculators and resources to help you tackle complex mathematical problems effortlessly.
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