Question

the border width of the square window frame is 0.3 m and the inside width is 1.2 m. what is the area of this border?

Explanation:

Step1: Find the side length of the outer square

The inside width is \( 1.2 \, \text{m} \), and the border width is \( 0.3 \, \text{m} \) on both sides. So the side length of the outer square \( a = 1.2 + 0.3\times2 = 1.2 + 0.6 = 1.8 \, \text{m} \)

Step2: Calculate the area of the outer square

The area of a square is \( \text{side length}^2 \), so the area of the outer square \( A_{\text{outer}} = 1.8^2 = 3.24 \, \text{m}^2 \)

Step3: Calculate the area of the inner square

The inside width is \( 1.2 \, \text{m} \), so the area of the inner square \( A_{\text{inner}} = 1.2^2 = 1.44 \, \text{m}^2 \)

Step4: Calculate the area of the border

The area of the border is the area of the outer square minus the area of the inner square, so \( A_{\text{border}} = A_{\text{outer}} - A_{\text{inner}} = 3.24 - 1.44 = 1.8 \, \text{m}^2 \)

Answer:

The area of the border is \( 1.8 \, \text{square meters} \)