Question

(b)Find the area and perimeter of a square whose diagonal is 10 cm

long.



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Answer 1

Answer:

(You can refer the diagram in the attachment)

Let the square be named ABCD with AC as its diagonal
Value of AC = 10 cm

Therefore a right angle triangle is formed
Let the sides of the triangle be x cm

Applying Pythagoras Theoram:
X^2 + X^2 = 10^2
2X^2 = 100
X^2 = 50 ....1)

Now formula of the area of the square is side^2
And since side = x here
Therefore side^2 = x^2
So area = x^2
Therefore area = 50 cm ( From 1)

Now the formula of perimeter = 4 * side
Therefore perimeter = 4 * root of 50
= 4 * root 25 *2
= 4 * root 5 * 5 * 2
= 4 * 5 root 2
= 20 root 2

Final Answer :
Area = 50 cm
Perimeter = 20 root 2 cm

Hope it helped!
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