question_answer 1)

Find the perimeter of each of the following figures. TIPS Perimeter is the distance covered along the boundary forming a closed figure when we go round the figure once. So, to find perimeter, add the length of all sides (which are line segments) of the given figure.

Answer:

(a) Let the given figure be ABCD. Here, \[AB=5\text{ }cm,BC=1cm,CD=2cm\]and \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DA\] \[=5cm+1cm+2cm+4cm=(5+1+2+4)\] \[cm=12cm\] Hence, the perimeter of the given figure is 12 cm. (b) Let the given figure be ABCD. Here, \[AB=23cm,BC=35cm,\] \[CD=40\,cm\] and \[DA=35\,cm\] \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DA\] \[=23cm+35cm+40cm+35cm\] \[=(23+35+40+35)cm=133cm\] Hence, the perimeter of the given figure is 133 cm. (c) Let the given figure be ABCD. Here, \[AB=5C=CD=DA=15cm\] \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DA~\] \[=15cm+15cm+15cm+15cm~\] \[=(15+15+15+15)cm=60cm\] Hence, the perimeter of the given figure is 60 cm. (d) Let the given figure be ABCDE. Here, \[~AB=BC=CD=DE=EA=4\,cm\] \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DE+EA\] \[=4cm+4cm+4cm+4cm+4cm\] \[=(4+4+4+4+4)cm=20cm\] Hence, the perimeter of the given figure is 20 cm. (e) Let the given figure be ABCDEFG. Here, \[AB=4cm,BC=0.5cm,CD=25cm,DE\] \[=25cm,\] \[EF=05\,cm,FG=4cm\] and \[GA=1cm\] \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DE+EF+FG+GA\] \[=4cm+0.5cm+2.5cm+2.5cm+0.5cm+4\] \[cm+1cm\] \[=(4+0.5+2.5+2.5+0.5+4+1)cm=15cm\] Hence, the perimeter of the given figure is 15 cm. (f) Let the given figure be named as shown below : Here, AB = FG = KL = PQ = 1 cm \[BC=DE=GH=IJ=LM=NO=QR=ST=3cm\]\[CD=HI=MN=RS=2cm\] \[~EF=JK=OP=TA=4cm\] \[\therefore \] Perimeter of the given figure = Sum of the lengths of all sides \[=AB+BC+CD+DE+EF+FG+GH+HI\] \[+IJ+JK+KL+LM+MN+NO+OP+PQ\]\[+QB+RS+ST+TA\] \[=(1+3+2+3+4+1+3+2+3+4+1\]\[+3+2+3+4+1+3+2+3+4)cm\] \[=52cm\] Hence, the perimeter of the given figure is 52 cm.