Final answer:
To find the area and perimeter of a square with a diagonal of 26 inches, use the Pythagorean theorem. The perimeter is 67.976 inches.
Step-by-step explanation:
To find the area and perimeter of the square, we need to determine the side length of the square. The diagonal of a square forms a right angle with two sides, so we can use the Pythagorean theorem to find the side length. Let's call the side length 's'. The diagonal of the square is 26 inches, so we can use the formula s² + s² = 26² to solve for 's'.
2s² = 26²
s² = 26² / 2
s² = 338
s = √338
Now that we have the side length, we can find the area and perimeter of the square. The area is found by multiplying the side length by itself, so the area is s * s = (√338)² = 338 square inches. The perimeter is found by adding up all four sides of the square, so the perimeter is 4 * s = 4 * √338
= 67.976 inches.