Respuesta :

Answer:

996 in²

Step-by-step explanation:

The figure is composed of a square and a triangle.

Using Pythagoras' identity on one of the right triangles within the triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

let the base of the right triangle be x, then

x² + 35² = 37², that is

x² + 1225 = 1369 ( subtract 1225 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Thus the base of the upper triangle = 2x = 2 × 12 = 24

Area of upper triangle = 0.5 bh ( b is the base and h the height )

Area = 0.5 × 24 × 35 = 12 × 35 = 420 in²

The length of the side of the square is therefore 24 in

Area = 24 × 24 = 576

Total area = 576 + 420 = 996 in²

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