Question

find the area of square the length of whose diagonal is 9.6 metre​

Answer 1

Answer:

A =46.08m² is the answer . The diagonal of a square is the line stretching from one corner of the square to the opposite corner. To find the diagonal of a square, you can use the formula {\displaystyle d=s{\sqrt {2}}}d=s{\sqrt {2}}, where {\displaystyle s}s equals one side length of the square. Sometimes, however, you might be asked to find the length of the diagonal given another value, such as the perimeter or area of the square. In these instances it is necessary to use different formulas first, so that you can determine the side length before using the diagonal formula.You Know the Length of One Side

Image titled Calculate a Diagonal of a Square Step 1

1

Find the length of one side of the square. This will probably be given to you. If you are working with a square in the real world, use a ruler or piece of measuring tape to find the length. Since all four sides of the square are the same length, you can use any side of the square. If you do not know the length of one side of the square, you cannot use this method.

For example, you might want to find the length of the diagonal of a square that has sides 5 centimeters long.

Image titled Calculate a Diagonal of a Square Step 2

2

Set up the formula d=s2{\displaystyle d=s{\sqrt {2}}}d=s{\sqrt {2}}. In the formula {\displaystyle d}d equals the length of the diagonal and {\displaystyle s}s equals one side of the square.[1]

This formula is derived from the Pythagorean Theorem ({\displaystyle a^{2}+b^{2}=c^{2})}a^{2}+b^{2}=c^{2}). A diagonal divides a square into two congruent right triangles, thus, you can use the side lengths of the square to find the length of the diagonal (which would be the hypotenuse of the right triangle).

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3

Plug the side length of the square into the formula. Make sure you are substituting for the variable {\displaystyle s}s.

For example, if the square has a side length of 5 centimeters, set up the formula like this:

{\displaystyle d=5{\sqrt {2}}}d=5{\sqrt {2}}