calculate the area of the shaded region in each of the figures gives below
40 m
22 m
18 m
22 m
Answers
Area of shaded region=arΔABC−arΔDBC
arΔABC=
s(s−a)(s−b)(s−c)
s=
2
a+b+c
=
2
122+22+120
=132m
∴arΔABC=
132(132−122)(132−22)(132−120)
=
132×10×110×12
=
11×12×10×10×11×12
=10×11×12=1320m
2
arΔBDC=
s(s−a)(s−−b)(s−c)
s=
2
a+b+c
=
2
36+22+24
=36m
∴arΔBDC=
36(36−26)(36−22)(36−24)
=
36×10×14×12
=
12×3×2×5×2×7×12
=2×12
105
=24×10.24=245.76m
2
∴ area of shaded region=1320−245.76=1074.24m
2
≈1074m
2
solution
Area of shaded region=arAABC-arADBC
46+28%
arAABC=
s(s-a)(s-b)(s-c)
2 a+b+c
2 122+22+120
=132m
MarAABC=
132(132-122)(132-22)(132-120)
132×10×110×12
11x12 10x10x11×12
=10×11-12=1320m
2
arABDC= s(s-a)(s--b)(s-c)
2
a+b+c
2
36+22+24
=36m
++arABDC= 36(36-26)(36-22)(36-24)
36×10×14×12
12×3×2×5×2×7×12
=2×12
105
=24×10.24-245.76m
2
..area of shaded region=1320-245.76-1074.24m
2
=1074m
2