Question

The length of a side of a square garden ABCD is 70m A minor segment of circle (o, OA) is drawn on each of the two opposite sides for developing lawn as shown in figure find the area of the lawn

Answer 1

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Answer 2

Answer:

The Area of the lawn is 2793 square meters .

Step-by-step explanation:

Given as :

The length of side of square ABCD = 70 m

A minor segment of circle is drawn on each opposite side of square

From figure drawn

mark the four unshaded portion by I , II , III , IV

Total area of portion I and III = Area of square ABCD - Area of semi-circle with diameter BC - Area of semi-circle with diameter AD

Or, Total area of portion I and III = [ 70 × 70 - $\dfrac{\pi 35^{2} }{2}$ -  $\dfrac{\pi 35^{2} }{2}$ ]

Or, Total area of portion I and III = [ 4900 - $\dfrac{3.14\times 1225}{2}$ - $\dfrac{3.14\times 1225}{2}$ ]

Or, Total area of portion I and III = [ 4900 - 3846.5 ]

Or, Total area of portion I and III = 1053.5 m²

Again

As The figure is a square so

The Total area of portion II and IV = 1053.5 m²

∴ Total area which is unshaded = Sum of area of portion I , II , III , IV

So, Total area which is unshaded = 1053.5 m² + 053.5 m²

i.e  Total area which is unshaded = 2107 m²

Now, Total Area of the shaded portion = Area of square - Total area which is unshaded

Or, Total Area of the shaded portion = 4900 m² - 2107 m²

Or, Total Area of the shaded portion = 2793 m²

Hence, The Area of the lawn is 2793 square meters . Answer