Mathematics
Find the area and perimeter of the figure (iii) given below in which all corners are right angles and all measurements are in cm.
Answer
The points are labelled on the figure as shown below:
Area of rectangle BCDE = l × b
= ED × CD
= 5 × 2
= 10 cm2.
Area of rectangle FGHI = l × b
= FG × GH
= 3 × 2
= 6 cm2.
Area of rectangle JKLM = l × b
= JK × KL
= 5 × 2
= 10 cm2.
Area of rectangle ABMN = l × b
= AB × AN
(From figure AB = AC - BC = 7 - 5 = 2 cm.)
= 2 × 12
= 24 cm2.
From figure,
Total area = Area of rectangle BCDE + Area of rectangle FGHI + Area of rectangle JKLM + Area of rectangle ABMN
= 10 + 6 + 10 + 24
= 50 cm2.
From figure,
The vertical distance between C and L will be equal to vertical distance between A and N,
So ignoring the vertical sides in right side and replacing it will CL.
Perimeter = AC + DE + FG + HI + JK + LN + NA + CL
= 7 + 5 + 3 + 3 + 5 + 7 + 12 + 12
= 54 cm.
Hence, area = 50 cm2 and perimeter = 54 cm.
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