Find the area of the squar obtained by joining the mid-point of the sides of the squar of area 36 sq.cm
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hello,
given below shows a figure ABCD in which P, Q, R and S are the midpoints of sides AB, BC, CD and AD.
we have that:
area of square ABCD=36 cm²
so each side is equal to:
AB=BC=CD=DA=√36= 6 cm
Now:
AP=AB:2=6:2=3 cm
similary,
AS=AD:2=6:2=3 cm
using Pythagoras theorem in triangle SAP,
we calculate the hypotenuse:
SP=√AP²+AS²=√3²+3²=√9+9=√18 cm
Since,PQRS is a square, so we have:
each side=L=SP=SR=RQ=PQ=√18 cm
we calculate the area of square PQRS:
A=L²=(√18)²=18 cm²
therefore area of the square obtained is 18 cm²
bye :-)
given below shows a figure ABCD in which P, Q, R and S are the midpoints of sides AB, BC, CD and AD.
we have that:
area of square ABCD=36 cm²
so each side is equal to:
AB=BC=CD=DA=√36= 6 cm
Now:
AP=AB:2=6:2=3 cm
similary,
AS=AD:2=6:2=3 cm
using Pythagoras theorem in triangle SAP,
we calculate the hypotenuse:
SP=√AP²+AS²=√3²+3²=√9+9=√18 cm
Since,PQRS is a square, so we have:
each side=L=SP=SR=RQ=PQ=√18 cm
we calculate the area of square PQRS:
A=L²=(√18)²=18 cm²
therefore area of the square obtained is 18 cm²
bye :-)
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