In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____

c
m
2

.

Question

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____

c
    m
    2

.

Accepted Answer

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is 40

c
    m
    2

.Given ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm.Applying Pythagoras theorem in triangle ADL,

hypotenou
    s
    2
   
   =bas
    e
    2
   
   +perpendicula
    r
    2

A
        D
        2

=A
        L
        2
       
       +D
        L
        2

5
        2

=
        4
        2
       
       +D
        L
        2

D
        L
        2

=
        5
        2
       
       −
        4
        2

DL

=
        
         25−16

DL

=
        9

DL

=3 cm

Applying Pythagoras theorem in triangle BCM,

hypotenou
    s
    2
   
   =bas
    e
    2
   
   +perpendicula
    r
    2

B
        C
        2

=B
        M
        2
       
       +M
        C
        2

5
        2

=
        4
        2
       
       +M
        C
        2

M
        C
        2

=
        5
        2
       
       −
        4
        2

MC

=
        
         25−16

MC

=
        9

MC

=3 cm

Now length DC is,

DC=DL+LM+MC

DC=3+7+3

DC=13 cm

Area of trapezium is,

A=
        
         h(a+b)
        2

A=
        1
        2
       
       ×(AB+DC)×AL

A=
        1
        2
       
       ×(7+13)×4

A=40 
        
         cm
        2

Area of trapezium is 40

c
    m
    2

.

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ $c m 2$ .

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In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ c m 2 .

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In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ $c m 2$ .