Question

diagrams on C D E F is a trapezium abcf is a rectangle BD is equal to 9 CM ab is equal to 6 CM EF is equal to 3 cm perimeter of abcf is equal to 20 centimetre calculate the area of trapezium CDEF​

Answer 1

Area of Trapezium is 24 $cm^2$

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)

⇒ $\frac {20}{2}$ = 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 = $\frac {1}{2} \times (Sum\ of\ Parallel\ Sides) \times Height$

= $\frac {1}{2} \times (CD + EF) \times CF$

= $\frac {1}{2} \times (5 + 3) \times 6$

= $\frac {8}{2} \times 6$

= $4 \times 6$  

= 24 $cm^2$