Question

d) area: 72 cm² area: 44 cm² area: ?

Explanation:

Step1: Recall Pythagorean theorem for squares

If the sides of the squares are \(a\), \(b\), and \(c\) such that the areas of the squares are \(A_1=a^{2}\), \(A_2 = b^{2}\), \(A_3=c^{2}\), and the right - angled triangle has sides \(a\), \(b\), \(c\) (where \(c\) is the hypotenuse), then \(a^{2}+b^{2}=c^{2}\) according to the Pythagorean theorem. In terms of areas of the squares on the sides of the right - angled triangle, if the area of the larger square is \(A_1\), and the areas of the other two squares are \(A_2\) and \(A_3\), then \(A_1=A_2 + A_3\) or \(A_2=A_1 - A_3\).

Step2: Calculate the unknown area

Let the area of the square with area \(72\ cm^{2}\) be \(A_1\), the area of the square with area \(44\ cm^{2}\) be \(A_3\), and the unknown area be \(A_2\). Then \(A_2=A_1 - A_3\). Substitute \(A_1 = 72\ cm^{2}\) and \(A_3=44\ cm^{2}\) into the formula. So \(A_2=72 - 44\).
\[A_2 = 28\ cm^{2}\]

Answer:

\(28\ cm^{2}\)