In the following figure, the square A B C D is divided into five … - Vidyadip

Question

In the following figure, the square $A B C D$ is divided into five equal parts, all having same area. The central part is circular and the lines $A E, G C, B F$ and HD lie along the diagonals $A C$ and $B D$ of the square. If $A B=22 cm$, find:
The perimeter of the part $ABEF$.

✓

Answer

We have a square $ABCD.$

We have,
$AB = 22cm$
We have to find the perimeter of ABEF. Let O be the centre of the circular region.Use Pythagoras theorem to get,
$2 (AE + r)^2 = 22^2$
$AE + r = 15.56$
$AE = (15.56 - 5.56)$cm
$=10c,$
Similarly,
BF = 10cm
Now length of arc EF,
$=\frac{\text{Perimeter of circular region}}{4}$
$=\frac{34.88}{4}\text{cm}$
= 8.64cm
So, perimeter of ABFE,
$= AB + BF + EF + AE$
$= 50.64cm$

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