Question

the area of the largest square in the figure is ((g + h)^2). use this figure to write the area of the largest square as the sum of the areas of the smaller squares and rectangles.
the area is (square). (simplify your answer.)

Explanation:

Step1: Identify smaller shapes' areas

The figure has two squares with areas $g^2$ and $h^2$, and two rectangles each with area $g \times h = gh$.

Step2: Sum all smaller areas

Add the areas of the four shapes together.
$g^2 + gh + gh + h^2$

Step3: Combine like terms

Simplify by merging the identical rectangle area terms.
$g^2 + 2gh + h^2$

Answer:

$g^2 + 2gh + h^2$