Question

Find the area of squares (in cm²) whose diagonals are of the following lengths:
(i) 12 cm
(ii) 2.5 m
(iii) 0.18 dm
[Hint: 1 m = 100 cm, 1 dm = 10 cm]​

Answer 1

Answer:

0.18 cm

is the correct answer

Answer 2

Answer:

(i) 72 cm²

(ii) 31250 cm²

(iii) 1.62 cm²

Step-by-step explanation:

Let us 1st see a generalised picture of this Question.

Let us take a square who has a side length of 's' units.

Then,

Its Area = s × s = s²

Now, we know that,

Square is a Quadrilateral with all of its angles equal to 90°.

Thus,

If we draw a diagonal on a square, then it would form two right triangles.

(Please do Refer the above image)

Now,

Let the diagonal have a length of 'd' units.

Then,

By Pythagoras theorem,

s² + s² = d²

2s² = d²

s² = d²/2

We know that,

s² = Area of the Square.

So,

Area = d²/2

Now, let's come back to our Original Question,

(i)

Diagonal (d) = 12 cm

So,

Area = d²/2

Area = 12²/2

Area = (12 × 12)/2

Area = 144/2

Area = 72 cm²

(ii)

Diagonal (d) = 2.5 m

But we are required to give the answer in cm²

So,

1 m = 100 cm

2.5 m = 2.5 × 100

2.5 m = 250 cm

d = 250 cm

Area = (250²)/2

Area = (250 × 250)/2

Area = 62500/2

Area = 31250 cm²

(iii)

Diagonal = 0.18 dm

But we are required to give the answer in cm²

So,

1 dm = 10 cm

0.18 dm = 0.18 × 10

0.18 dm = 1.8 cm

d = 1.8 cm

Area = d²/2

Area = (1.8²)/2

Area = (1.8 × 1.8)/2

Area = 3.24/2

Area = 1.62 cm²

Hope it helped and believing you understood it........All the best