Question

Please answer asap with an explanation

Answer 1

Answer:

The area of the given figure is $66.5\ cm^2$.

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 = $length\times breadth=length\ of AE\timeslength\ of DE$

Area of ABDE = $7\times8=56\ cm^2$

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 = $11-8=3\ cm$

Area of triangle BCD = $\frac{1}{2}\times base\times height}=\frac{1}{2}\times length\ of\ BD\times length\ of\ GF$

Area of BCD =  $\frac{1}{2}\times7\times3=\frac{21}{2}=10.5\ cm^2$

Area of ABCDE = Area of ABDE + Area of BCD = $56+10.5=66.5\ cm^2$

Thus the area of the given figure is $66.5\ cm^2$.