Question

diagnol of sqaure 16 cm find its area
​

Answer 1

→Question:  The Diagonal of square is 16 cm find its area ?

→Solution:

⇔Given: Diagonal of square = 16cm

⇔To find: Area of square = ?

⇔ a² + a² = d²   ( Diagonal and Area relation)

where,

• a =  area ( perpendicular or length of base )
• d = diagonal ( hypotenuse )

⇔ 2a² = d²

⇔ 2a² = 16²

⇔ 2a² = 256

⇔ a² =   ²⁵⁶⁄₂

⇔ a² = 128

⇔ a = √128

⇔ a =  √128    ( which is side)

⇔ Area = s²

⇔ Area = √128 × √128

⇔ Area = 128 ( √ and √ cancel )

⇔ Area = 128cm²

Another method:

⇔ Area of square with diagonal = 1 ÷ √2 Diagonal × 1 ÷ √2 Diagonal

⇔ Area of square with diagonal = 1 ÷ 2 × Diagonal²

⇔ Area of square with diagonal = 1 ÷ 2 × 16²

⇔ Area of square with diagonal =  ²⁵⁶⁄₂

∴ Area = 128cm²

∴ The area of square with diagonal 16cm is 128cm²

Answer 2

Answer:

2a² = d²

⇔ 2a² = 16²

⇔ 2a² = 256

⇔ a² =   ²⁵⁶⁄₂

⇔ a² = 128

⇔ a = √128

⇔ a =  √128    ( which is side)

⇔ Area = s²

⇔ Area = √128 × √128

⇔ Area = 128 ( √ and √ cancel )

⇔ Area = 128cm²

Step-by-step explanation: