Home
Class 12
MATHS
Three sides of a trapezium are each equ...

Three sides of a trapezium are each equal to 6 cm. Let `alpha in (0,pi/2)` be tha angle between a pair of adjacent sides.
What is the maximum area of the trapezium ?

A

`36sqrt(3) cm^(2)`

B

`30sqrt(3)cm^(2)`

C

`27sqrt(3) cm^(2)`

D

`24sqrt(3) cm^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Area `= (6+x) sqrt(36-x^(2))`
`= (6+3) sqrt(36-3^(2))`
`= 9sqrt(36-9)`
`= 9sqrt(27)`
`= 9sqrt(9xx3)`
`=27sqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    NDA PREVIOUS YEARS|Exercise DIRECTIONS|60 Videos

  • CONICS - PARABOLA, ELLIPSE & HYPERBOLA

    NDA PREVIOUS YEARS|Exercise MATH|62 Videos

  • DERIVATIVES

    NDA PREVIOUS YEARS|Exercise MCQs|94 Videos

Similar Questions

Explore conceptually related problems

Three sides of a trapezium are each equal to 6 cm. Let alpha in (0,pi/2) be tha angle between a pair of adjacent sides. If the area of the trapezium is the maximum possible, then what is alpha equal to ?

Three sides of a trapezium are each equal to 6 cm. Let alpha in (0,pi/2) be tha angle between a pair of adjacent sides. If the area of the trapezium is maximum, what is th length of the fourth side ?

Three sides of a trapezium are each equal to kcm. Find the greatest possible area of the trapezium.

The parallel sides of a trapezium are 30 cm and 20 cm and the area of it is 450cm^(2) , the distance between the parallel sides is

The length of the parallel sides of a trapezium are 51 cm and 21 cm , and that of each of the other two sides is 39 cm. What is the area ( in cm^(2) ) of the trapezium ?

The parallel sides of a trapezium are 48 cm, 40 cm, and the distance between them is 14 cm. Find the radius of a circle whose area is equal to the area of the trapezium.

NDA PREVIOUS YEARS-DEFINITE INTEGRATION & ITS APPLICATION-DIRECTIONS
  1. What is int(0)^(2pi) sqrt(1+ sin'x/2) dx equal to ?

    Text Solution

    |

  2. The area bounded by the curve |x | + |y| = 1is

    Text Solution

    |

  3. Let f(n) = [1/4 + n/1000], where [x] denote the integral part of x. ...

    Text Solution

    |

  4. The value of int(0)^(pi/4) sqrt(tanx) dx+int(0)^(pi/4) sqrt(cotx) dxis...

    Text Solution

    |

  5. What is the area of the region bounded by theparabolas y^2 = 6 (x - 1)...

    Text Solution

    |

  6. Three sides of a trapezium are each equal to 6 cm. Let alpha in (0,pi...

    Text Solution

    |

  7. Three sides of a trapezium are each equal to 6 cm. Let alpha in (0,pi...

    Text Solution

    |

  8. Three sides of a trapezium are each equal to 6 cm. Let alpha in (0,pi...

    Text Solution

    |

  9. What is int(0)^(pi)e^(x) sin x dx equal to ?

    Text Solution

    |

  10. What is int(1)^(e) xln x dx equal to ?

    Text Solution

    |

  11. What is int(0)^(sqrt(2))[x^(2)] dxequal to (where [.] is the greatest ...

    Text Solution

    |

  12. What is the value of int((-pi)/(4))^(pi/4) (sin xx tan x) dx ?

    Text Solution

    |

  13. If int(a)^(b)x^(3) dx = 0 and int(a)^(b) x^(2) dx = 2/3 then what are ...

    Text Solution

    |

  14. What is int(0)^(1)x (1-x)^(9) dx equal to ?

    Text Solution

    |

  15. what is inta^b [x] dx+inta^b [-x] dx equal to

    Text Solution

    |

  16. What is int(2)^(8) |x-5|dx equal to ?

    Text Solution

    |

  17. What is int(-1)^(1) {d/(dx) (tan^(-1)'1/x)} dx equal to ?

    Text Solution

    |

  18. int(0)^(pi/2) |sinx - cosx |dx is equal to

    Text Solution

    |

  19. int(0)^(pi//2) e^(sin)x cos xdx is equal to

    Text Solution

    |

  20. What is the area of one of the loops between the curve y = c sin x and...

    Text Solution

    |