Question

what is area of the large square? pythagorean theorem a = a1 + a2 + a3 + a4 + a5 (a+b)(a+b) = (a+b)² 4ab a² + b² 2ab

Explanation:

Step1: Determine side length of large square

The large square has a side length equal to \(a + b\) (since one side is composed of a segment of length \(a\) and a segment of length \(b\)).

Step2: Calculate area of square

The formula for the area of a square is \( \text{side length} \times \text{side length} \). So, the area \( A \) of the large square with side length \( a + b \) is \( (a + b)(a + b) \), which simplifies to \( (a + b)^2 \) using the formula for squaring a binomial.

Answer:

\((a + b)(a + b) = (a + b)^2\)