Question

B The area
of squarc is 16200 m²
find the length of diagonal​

Answer 1

Given :-

• The figure is a square
• Area of the square is 16200m²

To find :-

The diagonal of the square

Properties of a Square :-

• All sides are equal
• Diagonals bisect each other
• All the angles are equal (90°)
• Diagonals bisect each other at 90°
• It is a parallelogram

Method 1 :-

As we know that when the square is divided into 2 triangles, it forms 2 right angled triangles.

If we use the Pythagoras theorem, then the diagonal is the hypotenuse

Pythagoras theorem :-

The Pythagoras theorem states that the sum of base squared and height squared will be equal to the hypotenuse squared in a right angled triangle

• Hypotenuse is the longest side of the right angled triangle

Let the side be a

according to the theorem,

a² + a² = (diagonal)²

2a² = (diagonal)²

${a}^{2} = \dfrac{ ({diagonal})^{2} }{2}$

Hence we can say that the area of the square will be diagonal squared divided by 2.

The question has given us the area of the square and we have to find the diagonal

Let the diagonal be x

By substituting the values,

$16200 = \dfrac{ {x}^{2} }{2}$

By transposing 2 to the LHS (Left Hand Side)

$16200 \times 2 = {x}^{2}$

$32400 = {x}^{2}$

Transposing the power,

$\sqrt{32400} = x$

$180 = x$

Hence the length of the diagonal is 180m

Method 2 :-

Since we know the area of the square, we can find the side of the square and follow the Pythagoras theorem.

Area = 16200m²

$side = \sqrt{16200}$

$side = 90 \sqrt{2} \: m$

Now by applying the theorem,

$(90 \sqrt{2})^{2} + {(90 \sqrt{2}) }^{2} = {x}^{2}$

$16200 + 16200 = {x}^{2}$

$32400 = {x}^{2}$

Transposing the power,

$\sqrt{32400} = x$

$180 = x$

Some more formulas :-

Area of a parallelogram = base × height

Area of a rectangle = length × breadth

Area of a rhombus = ½ × Diagonal 1 × Diagonal 2

Area of a trapezium = ½ × Height × (sum of parallel sides)