Question

It is proposed to add two circular ends to a square lawn whose sides measure is 58cm the centre of a circle being

Answer 1

Question:

It is proposed to add to a square lawn measuring 58cm on a side ,two circular ends.the center of each circle is the point of intersection of the diagonals of the square. Find the area of the whole lawn.

Answer:

4325.14 cm²

Step-by-step explanation:

The diagonals of the square is the diameter of the circle

Find the area of the square:

Area = Length x Length

Area = 58 x 58

Area = 3364 cm²

Find the diagonal of the square:

a² + b² = c²

58² + 58² = c²

c² = 7=6728

c = √6728

c = 58√2 cm

Find the area of the whole circle:

Area = πr²

Area = π( 58√2  ÷ 2)²

Area = 1682π cm²

Find the area of the two segment:

Area = (1682π - 3364 ) ÷ 2 = 961.14 cm²

Find the area of the lawn:

Area = 3364 + 961.14 = 4325.14 cm²

Answer: 4325.14 cm²

Answer 2

Answer:

Step-by-step explanation:

Let ABCD be the square with AB = BC = CD = DA = 58 cm Area of square = AB × AC= 58 × 58 = 3364 sq cm We know that diagonals bisect each other at right angles in a square. ⇒ OA = OB = OC = OD and ∠AOB = ∠BOC = ∠COD = ∠DOA = 90° Diagonal of a square is √2 times its side That is AC = BD = 58√2 cm ⇒ OA = OB = OC = OD = 29√2 cm Area of segment AED = Area of sector OAEB – Area of triangle AOB à (1) Area of sector� Hence equation (1) becomes, Area of segment AED� Area of the whole lawn = Area of square + 2(area of two equal segments)