Question

A diagonal of a square tile is 10 mm. What is the area of the tile?

Answer 1

50 mm²

Explanation:

The diagonal divides the square into 2 right triangles, with the diagonal as the hypotenuse.

Using Pythagoras' identity in one of the right triangles.

let s be the side of the square, then

s² + s² = 10² = 100, that is

2s² = 100 ( divide both sides by 2 )

s² = 50 ( take the square root of both sides )

s =
`√(50)` =
`√(25(2))` = 5
`√(2)`

Thus

area = s² = (5
`√(2)` )² = 50 mm²

Answer 2

A=5×10-5m²

Explanation:

Unit Conversion:

d=0.01m

Using the formulas

A=a2

d=2a

Solving forA

A=1

2d2=1

2·0.012=5×10-5m²