there is a square the square is39m on both sides exept a 37m triangle in taking space now find the area of the shaded grey

Answer 1

To find the area of the shaded grey, we need to subtract the area of the 37m triangle from the total area of the square.

The area of the square is given by:
Area = side^2 = 39m * 39m = 1521m^2

The area of a triangle is given by:
Area = 1/2 * base * height

In this case, the base of the triangle is one side of the square (39m) and the height is the distance from the midpoint of the base to the top vertex of the triangle.

Since it's a right triangle, we can apply the Pythagorean theorem to find the height:
37m^2 = (39m/2)^2 + height^2
1369m^2 = 1521m^2/4 + height^2
height^2 = 1369m^2 - 1521m^2/4
height^2 = 1369m^2 - 380.25m^2
height^2 = 988.75m^2
height = √988.75m^2 ≈ 31.42m

Now we can find the area of the triangle:
Area = 1/2 * base * height = 1/2 * 39m * 31.42m ≈ 607.29m^2

Finally, to find the area of the shaded grey, we subtract the area of the triangle from the area of the square:
Shaded Grey = Total Area - Triangle Area = 1521m^2 - 607.29m^2 ≈ 913.71m^2

The area of the shaded grey is approximately 913.71 square meters.