Question

Find the area and length of the diagonal of the square having each following lengths. (Take √2 = 1.414)
(a) 8 cm
(b) 12 cm
(c) 3.5 m
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Answer 1

Step-by-step explanation:

We have been given the following lengths of each square.

1. Length = 8 cm
2. Length = 12 cm
3. Length = 3.5 cm

First of all, We will find area and length of diagonal for first length.

Case: 1

Area of a square is given by , Area = (Side)²

Area of Square = (8 cm)²

Area of Square = 64 cm²

0r

Length of diagonal of square is given by, d = s√2

d = 8√2 cm

d = 11.31 cm

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Case: 2

Area of Square = (Side)²

Area of Square = (12 cm)²

Area of Square = 144 cm²

0r

Length of diagonal of square = s√2

Length of diagonal of square = 12√2 cm

Length of diagonal of square = 16.97 cm

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Case: 3

Area of Square = (Side)²

Area of Square = (3.5cm)²

Area of Square = 12.25 cm²

0r

Length of diagonal of square = s√2

Length of diagonal of square = 3.5√2cm

Length of diagonal of square = 4.94 cm

Answer 2

Explanation: Before Solving the question, Let us discuss about some important formulae.

1. Area of Square = Side × Side, A = S²
2. Length of Diagonal of Square = Side × √2

Let's solve the problem:

We know that area of a square = (Side)²

Area of Square = (8)²

Area of Square = 64 cm²

Length of diagonal= Side√2

d = 8× √2 cm

d = 11.31 cm

Second Answer:

Area of Square = (12)²

Area of Square = 144 cm²

Length of diagonal = Side√2

Length of diagonal = 12× √2

Length of diagonal = 16.97 cm

Third Answer:

Area of Square = (3.5)²

Area of Square = 12.25 cm²

Length of diagonal= 3.5√2

Length of diagonal = 3.5 × √2

Length of diagonal=4.94 cm