In the figure (i) given below, two circular flower beds have been shown on the 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.
Mensuration
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Question

In the figure (i) given below, two circular flower beds have been shown on the 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.

Mensuration

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KnowledgeBoat · Accepted Answer

Area of lawn ABCD = (side)² = (56)² = 3136 m². In square, Length of diagonal (AC) = side = m. Since, diagonals of square are equal and bisect each other, ∴ AO = OC = OD = OB. Radius of quadrant ODC = Radius of quadrant OAB = m. Area of quadrant ODC = Area of quadrant OAB = Since, diagonals of square divide it into four equal triangles. Area of △ODC = Area of △OAB = = 784 m². From figure, Area of flower bed = Area of quadrant ODC - Area of △ODC = 1232 - 784 = 448 m². Since there are two flower beds so area = 2 × 448 = 896 m². Area of lawn and flower beds = 3136 + 896 = 4032 m². Hence, sum of the areas of the lawn and the flower beds = 4032 m².

Mathematics

In the figure (i) given below, two circular flower beds have been shown on the 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.

Mensuration

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