Question

CDEF is a trapezium, ABCD is a rectangle, BD = 14 cm, AB = 7 cm, EF = 4 cm, Perimeter of ABCF = 26cm Calculate the area of trapezium CDEF. You must show all your working

Answer 1

Answer:

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Answer 2

Answer:

Area of trapezium is 24cm²

Step-by-step explanation:

Given,

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 = 4 cm

Breadth of Rectangle, B = 4 cm (BC)

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

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

= 24 cm²