Please help me work this problem out I am stuck.
It's a square and in the top right corner there in another square inside it that is 1/4 the size of the big one. From that corner there is a diagonal line going to the other corner saying GD= 5in
The shaded area is the 3/4 that are not part of the little 1/4 square
Please help me
To solve this problem, we can first find the side length of the larger square. Since the smaller square is 1/4 the size of the larger square, its side length is 1/2 the side length of the larger square. Let's denote the side length of the larger square as x. Then the side length of the smaller square is x/2.
Since the diagonal GD divides the larger square into two right-angled triangles, we can apply the Pythagorean theorem to one of the triangles to find the side length of the larger square.
By the Pythagorean theorem, we have:
(x/2)^2 + (x/2)^2 = 5^2
x^2/4 + x^2/4 = 25
x^2/2 = 25
x^2 = 50
x = √50 ≈ 7.07 inches
Therefore, the side length of the larger square is approximately 7.07 inches.
Now we can calculate the area of the larger square by squaring the side length:
Area of larger square = (7.07)^2 = 50 square inches
The area of the smaller square is 1/4 of the area of the larger square:
Area of smaller square = (1/4)(7.07)^2 = 12.5 square inches
Since the shaded area is the 3/4 of the larger square that is not part of the smaller square, we can find it by subtracting the area of the smaller square from the area of the larger square:
Shaded area = 50 - 12.5 = 37.5 square inches
Therefore, the shaded area is approximately 37.5 square inches.