Question

there is a square the square is24m on both sides exept a 2m triangle in taking space now find the area of the shaded grey

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the shaded grey region, we need to subtract the area of the 2m triangle from the total area of the square.

The total area of the square is given by the formula: side length squared.

So, the total area of the square is 24m * 24m = 576 m².

The area of a triangle is given by the formula: base * height / 2.

In this case, the base of the triangle is 2m and the height is unknown. However, we can use the Pythagorean theorem to find the height.

Since the triangle is a right triangle (a triangle with one angle of 90 degrees), we can apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's call the height of the triangle "h". The hypotenuse is the diagonal of the square, which has a length of 24m.
Using the Pythagorean theorem, we have: h² + 2² = 24²
h² + 4 = 576
h² = 576 - 4
h² = 572
h ≈ √572
h ≈ 23.94m

Now that we know the height of the triangle, we can calculate its area:
Area of triangle = base * height / 2
Area of triangle = 2m * 23.94m / 2
Area of triangle ≈ 23.94m²

Therefore, the area of the shaded grey region is the total area of the square minus the area of the triangle:
Area of shaded grey region = 576m² - 23.94m²
Area of shaded grey region ≈ 552.06m²

So, the approximate area of the shaded grey region is 552.06 square meters.