Question

find the area of square the length of whose diagonal is 64 cm​

Answer 1

Answer:

2048 cm²

Step-by-step explanation:

Let diagonal of the square be d, side be s and area be A.

d² = s² + s² (By Pythagoras Theorem)

d² = 2 s²

d² = 2 A (Area of a square = side²)

64² / 2 = A

A = 32 × 64

A = 2048 cm²

Ans: The area is 2048 cm².

Hope this helps!

Answer 2

Area of the square is $2048 cm^{2} .$

• Any line segment that connects any two non-adjacent vertices is considered the diagonal of a square. Two diagonals that split at right angles and have equal lengths are found in a square.
• When the side length of a square is known, its diagonal can be calculated using the diagonal of square formula.
• The diagonal of a square is calculated using the formula d = $a\sqrt{2}$, where d is the diagonal and a is a square's side. The Pythagoras theorem is used to determine the diagonal of a square's formula.
• A square is split into two identical right-angled triangles by a diagonal. Both diagonals are congruent and form a right angle when they are divided.

Here, according to the given information, we are given that,

Length of the diagonal is given as 64 cm.

Now, we know that,

Area of a square = $\frac{1}{2} (diagonal)^{2}$

Then, we get,

Area of the square = $\frac{1}{2} (64)^{2} = 2048 cm^{2} .$

Hence, area of the square is $2048 cm^{2} .$

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