Question

In the given figure, ABCD is a rectangle and EF perpendicular to AB. The area of the shaded part, in the given figure, is

Answer 1

Answer:

In the given figure, ABCD is a rectangle, where AB=8 cm, BC=6 cm and the diagonals bisect each other at O. Find the area of the shaded region by Heron's formula

Given : AB=8cm BC=6cm

AC=

8

2

+6

2

=10

AO=

2

10

=5

S=

2

5+5+8

=9

Area of ΔAOB=

S(S−a)(S−b)(S−c)

=

9(9−8)(9−5)(9−5)

=

9×1×4×4

=3×4

Area of ΔAOB=12 sq. units

Answer 2

Given, AE=4cm,EB=8cm,BC=5cm

now, In triangle CBE

area of triangle = 1/2×b×h

=1/2×8×5

= 20cm²

Again,

In triangle DEF

area of triangle = 1/2×b×h

= 1/2×4×5

= 10cm²

area of shaded part = 20cm²+10cm²

= 30cm²