In a circle of radius 21 cm an arc subtends an angle of 72° at the centre. The length of the arc is?

Area of the sector = [(22/7) x 12 x 12] x [42°/360°] m²
= 52.8 m²

? ?d-d = 105 cm
? (? -1 ) d = 105 cm
? [(22/7)-1] x d = 105 cm
? d = (7/15) x 105 cm = 49 cm

? 2?R - 2?r = (176-132)
? 2?(R-r) = 44
? R-r = ( 44 x 7 )/ (2 x 22)
= 7 m

Area left ungrazed
= [(63 x 63) - (4 x 1/4 x 22/7 x (63/2)²] m²
= (63 x 63 - (99 x 63)/2 ) m²
= 63 x (63 - 99/2) m²
= 850.5 m²

Length of each side of hexagoan = radius of circle
? its perimeter = 6r

Area of sector = ( arc length x radius ) / 2 cm²
= (3.5 x 5 ) / 2
= 8.75 cm²

Let length = a metres and breadth = b metres
Then, 2(a+b)= 46
? (a+b) =23 and ab =120
? Diagonal = ?a² + b²
?(23)²-2 x 120
?289 = 17 m

Speed = 12 x (5/18) m/sec
=10/3 m/sec

there4; perimeter = (10/3) x 15 x 60 m=3000 m
? 2( a + 4a) = 3000 m
? a = 300 m
So, length = 1200 m and breadth = 300 m

? Area = (1200 x 300 ) m² = 360000m²

Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4^th of area of the original triangle .
So area of ? DEF = 36/ 4 = 9 m²

Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)

And from question d + l = 5b
? d = 5b - l ...(2)
? d² = 25b² + l² - 10 x lb
? l²+ b² = 25b² + l² - 10 x lb
? l²+b² = 25b² + l² - 10 x 60
? 24b² = 600
? b = ?25 = 5 m
? l = 60 / b = 60 / 5 = 12 m