Question

The lenth of a diagonal of a square is 6 root2cm. Find the lenth of its side and hence find the area of a square? ​

Answer 1

Question

The length of a diagonal of a square is 6√2 cm Find the length of its side and hence find the area of a square ?

Answer

Required measure for each side = 6 cm

Area of Square = 36 cm²

Figure

$\begin{gathered} \sf{ \red{6 \: cm} \:}\huge\boxed{ \begin{array}{cc} \: \: \\ \footnotesize{ \sf{square}}\: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{ \pink{6 \: cm}}\end{gathered}$

Solution

Here , the length of diagonal of a square = 6√2 cm and , what we have to calculate is the measure of its each side .

Let each side of a square be x cm

Now there are two methods for finding the value

Method 1

The direct application of formula for diagonal

Diagonal of Square = √2 × a

:↦ 6√2 = √2 × a

√2 will be cancelled from both sides

:↦ a = 6

Method 2

By applying the Pythagoras Theorem for that assume that if a diagonal is made to draw within the square it will form two right angled triangle . The Hypotenuse of which is 6√2 cm while both base and perpendicular is a cm

Applying Pythagoras Theorem

H² = P² + B²

:↦ (6√2)² = a² + a²

:↦ 72 = 2a²

:↦ 36 = a²

:↦ a = ±√36

:↦ a = 6 ( -ve sign can be ignored for a side can't be negative)

Now , from application of either of two methods we get the value for a = 6

Each measure for side of a square = 6 cm

Now for the calculation of Area of Square apply direct formula :-

Area of Square = (side)²

:↦ Area of Square = a²

:↦ Area of Square = 6²

:↦ Area of Square = 36 cm²

So , here we are all done with our calculation

$\underline{\rule{180pts}{2pts}}$

Thankyou

Answer 2

Answer

Required measure for each side = 6 cm

Area of Square = 36 cm²

Solution

Here , the length of diagonal of a square = 6√2 cm and , what we have to calculate is the measure of its each side .

Let each side of a square be x cm

Now there are two methods for finding the value

Method 1

The direct application of formula for diagonal

Diagonal of Square = √2 × a

:↦ 6√2 = √2 × a

√2 will be cancelled from both sides

:↦ a = 6

Method 2

By applying the Pythagoras Theorem for that assume that if a diagonal is made to draw within the square it will form two right angled triangle . The Hypotenuse of which is 6√2 cm while both base and perpendicular is a cm

Applying Pythagoras Theorem

H² = P² + B²

:↦ (6√2)² = a² + a²

:↦ 72 = 2a²

:↦ 36 = a²

:↦ a = ±√36

:↦ a = 6 ( -ve sign can be ignored for a side can't be negative)

Now , from application of either of two methods we get the value for a = 6

Each measure for side of a square = 6 cm

Now for the calculation of Area of Square apply direct formula :-

Area of Square = (side)²

:↦ Area of Square = a²

:↦ Area of Square = 6²

:↦ Area of Square = 36 cm²

So , here we are all done with our calculation