Math Problem Statement

Solve

What is the area of the shaded region in the image with two squares, where the side length of the larger square is 29.6 meters and the side length of the smaller square is 12.7 meters?

Solution

To find the area of the shaded region, we need to:

  1. Calculate the area of the larger blue square.
  2. Calculate the area of the smaller white square inside it.
  3. Subtract the area of the smaller square from the area of the larger square.

Step 1: Area of the larger square

The side length of the larger square is 29.6 meters.

Area of the larger square=(29.6)2=876.16 square meters\text{Area of the larger square} = (29.6)^2 = 876.16 \text{ square meters}

Step 2: Area of the smaller square

The side length of the smaller square is 12.7 meters.

Area of the smaller square=(12.7)2=161.29 square meters\text{Area of the smaller square} = (12.7)^2 = 161.29 \text{ square meters}

Step 3: Subtract the area of the smaller square from the larger square

Area of the shaded region=876.16161.29=714.87 square meters\text{Area of the shaded region} = 876.16 - 161.29 = 714.87 \text{ square meters}

Thus, the area of the shaded region is 714.87 square meters.

Would you like more details or have any other questions?


Here are some related questions for further practice:

  1. What is the perimeter of the larger square?
  2. What is the perimeter of the smaller square?
  3. If the larger square's side length were increased by 10%, what would be the new shaded area?
  4. How would the area of the shaded region change if the side of the smaller square were halved?
  5. What would be the area of the shaded region if both the smaller and larger squares were doubled in size?

Tip: Always remember to subtract the smaller area from the larger one when calculating areas for shaded regions like this!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation

Formulas

Area of a square = side × side
Shaded area = Area of larger square - Area of smaller square

Theorems

Basic properties of squares

Suitable Grade Level

Grades 6-8