Question

the area of a square ABCD is 64 square centimetre. find the area of square obtained by joining the midpoint of the side of the square ABCD

Answer 1

area of given square = 64cm²
a²=64
a=8cm [ side of given square]
a/2= 4cm

side of required square=a'
a'=√[a/2)²+(a/2)²]
=> √ (4² +4²)
=> √32
=>4√2 cm

Area of required square=(a')²
=>(4√2)²=>32cm²

Answer 2

area of square obtained by joining the midpoint of the side of the square ABCD = 32 cm²  if  area of a square ABCD is 64 cm²

Step-by-step explanation:

area of a square ABCD is 64 square centimetre

Area of square =- Side²

Side² = 64 cm²

=> Side = 8 cm

AB = BC = CD = DA = 8 cm

let say P , Q , R , S are midpoints of AB , BC , CD & DA

AP = BP = BQ = CQ = CR = DR = DS = AS = 8/2 = 4 cm

PQ² = BP² + BQ²  = 4² + 4²  = 32

similarly PQ = QR = PR = RS

Area of PQRS = PQ² = 32 cm²

Learn more:

The midpoints of the sides of a square of side 1 are joined to form a ...

https://brainly.in/question/12756025

ABCD is a square of sides 8cm . M is midpoint of side AB if MCN =45 ...

https://brainly.in/question/9575670