I have a square that is divided into 2 triangles. In the middle of the top triangle there is this: 6�ã2 in. and at the bottom corner of the same triangle it says 45 degrees. Could some explain to me how to find the area and the perimeter? I'm not sure what I'm supposed to do with the radical.
So the square has a diagonal whose length is 6√2 in. The angle made by the diagonals with the sides of a square is always 45° as stated.
If the side length of a square is x, then the length of the diagonal is x√2, which implies that the given square is of side length 6 inches.
Would you now be able to proceed to find the area and perimeter of a square of side length 6 inches?
Got it! Thanks so much!
To find the area and perimeter of the square, we need to understand how the given information relates to the shape.
Let's break down the steps to find the area and perimeter:
1. Determine the length of one side of the square:
Since the square is divided into two congruent triangles, the side length can be found by doubling the length given in the middle of the top triangle. In this case, the length is 6√2 inches. Thus, the side length of the square is 2 * 6√2 = 12√2 inches.
2. Calculate the area of the square:
The area of a square can be found by squaring its side length. Therefore, the area of the square is (12√2)^2 = 144 * 2 = 288 square inches.
3. Determine the perimeter of the square:
The perimeter of a square is found by multiplying its side length by 4. In this case, the perimeter is 12√2 * 4 = 48√2 inches.
So, the area of the square is 288 square inches and the perimeter is 48√2 inches.
Regarding the radical (√2), it is an irrational number approximately equal to 1.414. It is often encountered in geometric calculations involving right triangles, squares, or circles. In this case, it is used as a multiple for the given length in inches.