Square

 Find the Length of a side when the area of a square is given

a) 81cm^2

Solution

Given, 

Area of a square = 81cm^2

Formula 

Area of a square  = a^2 square units ( 'a' is the length of a side )

here, a^2 = 81cm^2

    to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(81cm^2)

 a = 9cm ( sqrt(81) = +/-9, but length of a side is always positive )

Hence the length of a side = 9cm

b) 0.25 dm^2

Solution

Given, 

Area of a square = 0.25 dm^2

Formula 

Area of a square  = a^2 square units ( 'a' is the length of a side )

here, a^2 = 0.25 dm^2

    to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(0.25 dm^2)

 a = 0.5 dm  

Hence the length of a side = 0.25 dm

c) 1.44 km^2

Solution

Given, 

Area of a square = 1.44 km^2

Formula 

Area of a square  = a^2 square units ( 'a' is the length of a side )

here, a^2 = 1.44 km^2

    to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(1.44 km^2)

 a = 1.2 km  

Hence the length of a side = 1.2 km

d) 2.25 ha

Given, 

Area of a square = 2.25 ha

we know that , 1 ha = 1000 m^2 (ha - hectare)

 

2.25 ha = 2.25 * 1000 m^2

            = 2250 m^2

so, now area of a square  = 2250 m^2

Formula 

Area of a square  = a^2 square units ( 'a' is the length of a side )

                   a^2 = 2250 m^2

          sqrt(a^2) = sqrt(2250 m^2)

                       a =  15sqrt(10) m

Note 

sqrt(2250) = sqrt(225*10)

                 = sqrt(225) * sqrt(10)

                 = 15 sqrt(10)

Hence the length of a side = 15 sqrt(10) m