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

Area of trapezium is 24cm²

Step-by-step 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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have