Question

in the given figure,ABCD is a piece of cardboard in the shape of a trapezium in which AB||DC, triangle ABC =90

Answer 1

here is your answer,

Answer 2

The area of the remaining piece of the cardboard is 7.98 $cm^2$.

Step-by-step explanation:

Given:

Here, ABCD is a piece of cardboard in the shape of a trapezium.

Also, AB║DC and ∠ ABC = 90°.

DC = BC = 4.2 cm, AE = 2 cm

To find:

The area of the remaining piece of the cardboard?

Solution:

As it is given  BEFC is a quarter circle.

Thus,  BC = BE = radius of the circle

BC = BE = DC =  4.2 cm.              [given]

Now, AB = AE + EB

              = 2 + 4.2

               = 6.2 cm

ABCD  is trapezium  and AB║DC and ∠ ABC = 90

Thus, area of trapezium  ABCD = $\frac{AB+CD}{2} \times BC$

                                                     = $\frac{6.2+4.2}{2} \times 4.2$

                                                     = $\frac{10.4}{2} \times 4.2$

                                                     = $5.2\times 4.2$

                                                     = $21.84 cm^2$

Area of the quarter circle = $\frac{\pi (BC)^2}{4}$

                                           = $\frac{\frac{22}{7} \times (4.2)^2}{4}$

                                            = $\frac{22\times 17.64}{7 \times 4}$

                                            = $13.86 cm ^2$

Thus, area of the shaded region = area of trapezium  ABCD - area of the quarter circle

                                                        = 21.84 - 13.86

                                                         = $7.98 cm^2$