The side of a square is 8 cm. Find the area of the square drawn on a diagonal of the original square (8 cm X 8 cm).
You need to find the length of side of the new square whose area you need to evaluate, hence, using the information provided by the problem, that the side of the new square is the diagonal of the original square, you need to remember the equation that relates the side of a square and its diagonal, such that:
`d = l sqrt 2`
`d` represents the length of diagonal of square
`l` represents the length of the side of the square
You need to evaluate the area of the new square, such that:
`A = d*d => A = d^2 => A = (l*sqrt 2)^2 => A = 2l^2`
You need to substitute `8 cm` for `l ` such that:
`A = 2*64 cm^2 => A = 128 cm^2`
Hence, evaluating the area of the new square, yields `A = 128 cm^2.`
ok. draw an 8x8 square then draw a diagonal line from corner to corner. Now You've got 2 identical right-angled triangles. We need to find the length of the diagonal line, which is also the hypotenuse for these 2 triangles. We know our triangles have sides 8cm and 8cm.
Pythagoras said for a right angle triangle A^2 + B^2 = C^2
so 8^2 + 8^2 = C^2
so 64 + 64 = C^2
so 128 = C^2
So C = 11.314cm
So your new square has sides 11.314cm
To find the area of this new square you multiply the sides.
So we get 128 again!
The answer is 128 sq.cm