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
