The cross section of a canal is a trapezium in shape . If the canal is a trapezium in shape. If the canal is 10 meters wide at the top and 6 meters wide at bottom and the area of cross section is 640 sq. meters The depth of canal is?

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

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

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

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

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

AB = 60 m, BC = 40 m and AC = 80 m
? s = (60 + 40 + 80 ) / 2 m = 90 m
(s-a) = 90 - 60 = 30 m,
(s-b) = 90 - 40 = 50 m and
(s-c) = 90 - 80 = 10 m

? Area of ? ABC =
?s(s-a)(s-b)(s-c)
= ?90 x 30 x 50 x 10 m²
= 300?15 m²

? Area of parallelogram ABCD = 2 x area of ? ABC
= 600?15 m²

AB = 6 cm ; AD = 4 cm and ? BAD = 30°
Area of parallelogram ABCD = AB x AD x sin 30°
= 6 x 4 x sin 30° = 12 cm²

Area of parallelogram = Side of parallelogram x distance from the opposite side
= 14 x 16 cm²
= 224 cm²