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Question

A composite figure is shown with the following measurements: on the left side is a 7cm length by 16cm width vertical rectangle, a 6cm by 4cm rectangle connects the first rectangle to an identical 7cm by 16cm rectangle on the right. In the center of the 16 cm width of the rectangle on the right is another small rectangle with a length of 5cm and width of 4 cm.

What is the area of the polygon?

(1 point)
Responses

112 square centimeters
112 square centimeters

400 square centimeters
400 square centimeters

70 square centimeters
70 square centimeters

268 square centimeters
268 square centimeters
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Answer 1

To find the area of the composite figure, we need to calculate the area of each rectangle and then combine those areas.

1. Calculate the area of the two large rectangles (7cm x 16cm).

   • Area of one rectangle = length × width = 7 cm × 16 cm = 112 cm²
   • Since there are two such rectangles: 112 cm² × 2 = 224 cm²

2. Calculate the area of the middle rectangle that connects the two large rectangles (6cm x 4cm).

   • Area = length × width = 6 cm × 4 cm = 24 cm²

3. Calculate the area of the small rectangle in the center of the right rectangle (5cm x 4cm).

   • Area = length × width = 5 cm × 4 cm = 20 cm²

Now, add all these areas together:

• Total area = Area of the two large rectangles + Area of the middle rectangle - Area of the small rectangle
• Total area = 224 cm² + 24 cm² - 20 cm² = 228 cm²

However, this value isn’t in your responses. Let's consider that you might need to combine the areas without subtracting the small rectangle—if it is part of the total area rather than deducted.

If I sum them instead (not treating the small rectangle as a subtraction but as part of the total)—it would be:

• Total area = 224 cm² + 24 cm² + 20 cm² = 268 cm²

Therefore, the area of the polygon is 268 square centimeters.