Question

ABCD is a trapezium ,CDEF is a parallelogram . Find the shaded region

Answer 1

area of trapezium=1/2*(sum of parallel sides)*height
=>1/2*(24+15)*8
=>39*4
=>156 cm square.
area of triangle=1/2*base*height
=1/2*6*8
=24 cm square
area of parallelogram=base*height
=6*14
=84 cm square
thus,
area of shaded region=156-(24+84)
". ". ". ". =156-108
=48 cm square

Answer 2

Area of shaded region is 48 square centimetre.

Step-by-step explanation:

Given:- ABCD is a trapezium with,

2 parallel sides AD and BC,

Height of trapezium AB=8 cm,

BG=6 cm, GC=9 cm,

CDEF is a parallelogram with,

Base CD=14 cm, height CH=6 cm.

To find:-Area of shaded region AGFE=?

Solution:-

Area of trapezium ABCD =   $\frac{1}{2} \times$ sum of parallel side$\times$ height

Area of trapezium ABCD = $\frac{1}{2} \times (AD+BC)\times AB$

Area of trapezium ABCD = $\frac{1}{2} \times(AD+(BG+FC))\times AB$   ---(∵ BC=BG+FC)

Area of trapezium ABCD = $\frac{1}{2} \times (24+6+9)\times 8$------(from given)

Area of trapezium ABCD = $\frac{1}{2}\times 39\times 8$

Area of trapezium ABCD = 39$\times$4

Area of trapezium ABCD = 156 sq.cm.  -----------------(1)

Now,

Area of $\triangle ABG$ = $\frac{1}{2}\times b\times h$

Area of  $\triangle ABG$  = $\frac{1}{2} \times BG\times AB$--------(∵ AB is height and BG is base)

Area of $\triangle ABG$ = $\frac{1}{2} \times 6\times 8$-----------(∵ AB=8 cm, and BG=6 cm. from figure)

Area of $\triangle ABG$ = $6\times 4$

Area of $\triangle ABG$ = 24 sq.cm. -----------------(2)

Now,

Area of parallelogram CDEF = $b\times h$  

Area of parallelogram CDEF = CD $\times$ CH  

Area of parallelogram CDEF = 14 $\times$ 6  ----------------(from given)

Area of parallelogram CDEF = 84 sq.cm.    --------------(3)

Now,

Area of shaded region = Area of trapezium ABCD - Area of    - Area of parallelogram CDEF

Area of shaded region = 156-24-84               -------------(from 1,2,3)

Area of shaded region = 48 sq.cm.

Therefore Area of shaded region is 48 square centimetre.