If D,E and F are respectively the midpoint of the sides BC , CA and AB of a ? ABC and the area of ? ABC = 36m ². Then area of ? DEF is?

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

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

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

Arc length = 2?r (?° / 360°)
= 2 x (22/7) x 21 x (72° / 360°) cm
= 26.4 cm

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

We know that area of triangle = ( base x height ) / 2
So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
? (10 x 4.4) / 2 = (11 x h) / 2
? h= (10 x 4.4)/11 = 4 cm

Cross section area = 1/2 x ( a + b ) x d
where a and b are the parallel sides, d is the perpendicular distance between them.
? 1/2 x ( a + b ) x d = 640
? d = (640 x 2) / 16 = 80m

Let the parallel sides be 3a and 5a.
So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.
? 1/2 (3a +5a) x 12 = 384
? 8a = 64
? a =8

? Smaller side = 3x = 3 x 8 = 24 cm.

Area of trapezium = 1/2 x sum of parallel sides x perpendicular distance between them
= 1/2 (1 + 2) x 6 m²
= 9 m²