# Areas of Combinations of Plane Figures

## Notes

So far, we have calculated the areas of different figures separately. Let us now try to calculate the areas of some combinations of plane figures.
Example 4 : In Fig., two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.

For sector ODC,
∠DOC= θ= 90° (because O is the point of intersection of diagonals of square ABCD
"Diagonal BD"= "side"sqrt2= 56sqrt2

therefore, OD=r = (56sqrt2)/2= 28sqrt2cm

area of sector ODC= θ/360 xx πr^2

=(90 xx 22 xx 28sqrt2 xx 28sqrt2)/360 xx 7

= 22 xx 2 xx 28

area of sector ODC= 22 xx 56m^2

area of ΔDOC= 1/2 xx OD xx OC

= 1/2 xx  28sqrt2 xx 28sqrt 2

area of ΔDOC= 19 xx 56m^2

area of flower beds= 2 xx (22 xx 56)- (19 xx 56)
= 2 xx 56  (22-19)
= 112 xx 8
area of flower beds= 896m^2
"area"   "of"   "lawn"= "side"^2= 56^2
"area"  "of"   "lawn"= 3136m^2
"Total"   "area" = 3136+896
"Total"   "area" = 4032m^2

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