Question

Find the area of a square whose diagonals are of
length 18 cm​

Answer 1

Correct Question-:

• Find the area of a square whose diagonals are of length 18 cm.

AnswEr-:

• Area of Square = 162 cm [ 161.7984] = [Approx Value]

Explanation-:

Given-:

• The Diagonal of a square is 18 cm .

To Find -:

• Area of a Square.

• By Analysing Attachment

we can see that -:

• ABCD is a Square and ,
• Triangle ️ ABC is a right angled triangle .

Then ,

• AC² = AB² + BC² _________[ By Applying Pythagoras Theorem]

Here,

• AC = Diagonal = 18 cm ______ [ Given That ]

Now ,

• (18)² = AB² + BC²

As we know that all sides of Square are equal.

• AB = BC = CD = DA

So ,

• AB = BC

Now ,

• (18)² = AB² + BC² or (18)² = AB² + AB²
• 324 = AB² + AB²
• 324 = 2AB²
• 324/2 = AB²
• 162 = AB²
• $\large{\sqrt{162} = AB}$
• 12.72 cm = AB __________[Approx]

Now ,

• AB = Side of a Square = 12.72 cm

Now ,

• Area of Square = Side × Side

Here ,

• Length of Side = 12.72 cm [Approx ]

Now ,

• Area of Square = 12.72 × 12.72
• Area of Square = 162 cm [ 161.7984] = [Approx Value]

Hence ,

• Area of Square = 162 cm [ 161.7984] = [Approx Value]

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