Question

ABCD is a rectangle CDEF is a trapezium AE is a straight line AB =9cm AE =11 cm and DE=5cm the perimeter of a rectangle ABCF is 28 cm calculate the area of the trapezium CDEF

Answer 1

Area of trapezium is 24cm²

Explanation:

The Perimeter of rectangle ABCF = 20 cm

One of the sides AB = 6 cm (AB)(Let it be L)

Let the other side of Rectangle be B.

We know that Perimeter of Rectangle = 2 (Length + Breadth)

So,

20 = 2(L+B) = 2(6 + B)

= 6+B

10 = 6+B

B = 10-6

B = 4cm

Breadth of Rectangle, B = 4cm (BC)

Length of side of trapezium, CD = BD - BC = 9 - 4= 5cm

And length of EF = 3 cm

Now, Sides, AB and EC act as Perpendicular for Trapezium CDEF (Sides of Rectangle are perpendicular to each other)

We know that,

Area of Trapezium = ½ × (sum of parallel sides )×height

= ½×(CD + EF)× CF

= ½×(5+3)×6

= 8/2 ×6

= 4×6

= 36 cm²

Area of trapezium = 24cm²