How do I figure out the area and perimeter of a square if all I know is the cross (top left corner to bottom right corner) measurement? I have a square with the cross measurement of 8.5 (or 4 X sq root of 2, i rounded to 8.5). The square looks like it is cut in half to look like 2 triangles and in the corner of one triangle it says 45 degrees.

Question

How do I figure out the area and perimeter of a square if all I know is the cross (top left corner to bottom right corner) measurement? I have a square with the cross measurement of 8.5 (or 4 X sq root of 2, i rounded to 8.5). The square looks like it is cut in half to look like 2 triangles and in the corner of one triangle it says 45 degrees.

Please help me, I am so confused, is there a formula to figure this problem out?

Answer 1

The diagonal (the slant of the triangle) of a square of side x is √2*x.

Can you figure the side using this relation?

Answer 2

I don't know what grade level you are in, but since you seem to know about square roots, I am somewhat surprised that you don't know the Pythagorean Theorem.

Since you are dealing with a square, let each side of the square be x

then x^2 + x^2 = (4√2)^2
2x^2 = 32
x^2 = 16
x = 4

Now that we know that we have a 4 x 4 square, we can easily find its area and perimeter.

Answer 3

BTW, how did you come up with 8.5 for 4√2 ?

Answer 4

To find the area and perimeter of a square, you need to know more than just the diagonal or the cross measurement. However, since you mentioned that the square is cut in half and one of the triangles has a 45-degree angle, we can use this information to find the missing values.

Here's how you can proceed:

1. Determine the length of one side: Since we have a right triangle with a 45-degree angle, we know that the other two angles are also 45 degrees each. In an isosceles right triangle (45-45-90 triangle), the ratio of the sides is 1:1:√2. Since you mentioned that the cross measurement is 8.5, it means that each leg of the triangle is half that value: 8.5/2 = 4.25. Therefore, the length of one side of the square is 4.25.

2. Calculate the area: The area of a square is given by side^2. In this case, the length of one side is 4.25. So, the area of the square is 4.25^2 = 18.0625 square units.

3. Find the perimeter: The perimeter of a square is calculated by multiplying the length of one side by 4. In this case, the length of one side is 4.25. So, the perimeter of the square is 4.25 x 4 = 17 units.

So, the area of the square is 18.0625 square units, and the perimeter is 17 units.

Note: If you had only been given the cross measurement without the information about the triangles and angles, it wouldn't have been possible to determine the area and perimeter of the square accurately.