Answer:
The area of the given figure is [tex]66.5\ cm^2[/tex].
Step-by-step explanation:
To find out the area we should have to redraw the figure having nomenclature ABCDE and join BD. Thus we have a rectangle ABDE and a triangle BCD.
The new figure is in the attachment.
Given,
Length of AE = 7 cm
Length of DE = 8 cm
Length of CF = 11 cm
Solution,
Area of rectangle ABDE = [tex]length\times breadth=length\ of AE\timeslength\ of DE[/tex]
Area of ABDE = [tex]7\times8=56\ cm^2[/tex]
Now for triangle BCD,
Length of BD = length of AE = 7 cm
Length of GF = Length of DE = 8 cm
∴ Length of CG = Length of CF-Length of GF = [tex]11-8=3\ cm[/tex]
Area of triangle BCD = [tex]\frac{1}{2}\times base\times height}=\frac{1}{2}\times length\ of\ BD\times length\ of\ GF[/tex]
Area of BCD = [tex]\frac{1}{2}\times7\times3=\frac{21}{2}=10.5\ cm^2[/tex]
Area of ABCDE = Area of ABDE + Area of BCD = [tex]56+10.5=66.5\ cm^2[/tex]
Thus the area of the given figure is [tex]66.5\ cm^2[/tex].
