What is the area of a polygon composed of two rectangles measuring 36 inches by 18 inches and 24 inches by 18 inches?

What is the area of a polygon composed of two rectangles measuring 36 inches by 18 inches and 24 inches by 18 inches?

• A. 21 square inches
• B. 54 square inches
• C. 1,008 square inches
• D. 1,080 square inches

Answer: (D)

To find the area of the polygon that consists of the two rectangles, first calculate the area of each rectangle separately and then sum those areas. The area of a rectangle can be calculated using the formula: Area = length × width. For the first rectangle, which measures 36 inches by 18 inches, the area is calculated as follows: Area of first rectangle = 36 inches × 18 inches = 648 square inches. For the second rectangle, which measures 24 inches by 18 inches, the area is: Area of second rectangle = 24 inches × 18 inches = 432 square inches. Now, add the areas of both rectangles together to find the total area of the polygon: Total area = Area of first rectangle + Area of second rectangle Total area = 648 square inches + 432 square inches = 1,080 square inches. This calculation confirms that the area of the polygon is indeed 1,080 square inches, which matches with the correct answer. Summing the areas of the individual rectangles accurately reflects the total area they occupy as part of the polygon's structure.

To find the area of the polygon that consists of the two rectangles, first calculate the area of each rectangle separately and then sum those areas.

The area of a rectangle can be calculated using the formula: Area = length × width.

For the first rectangle, which measures 36 inches by 18 inches, the area is calculated as follows:

Area of first rectangle = 36 inches × 18 inches = 648 square inches.

For the second rectangle, which measures 24 inches by 18 inches, the area is:

Area of second rectangle = 24 inches × 18 inches = 432 square inches.

Now, add the areas of both rectangles together to find the total area of the polygon:

Total area = Area of first rectangle + Area of second rectangle

Total area = 648 square inches + 432 square inches = 1,080 square inches.

This calculation confirms that the area of the polygon is indeed 1,080 square inches, which matches with the correct answer. Summing the areas of the individual rectangles accurately reflects the total area they occupy as part of the polygon's structure.