Question

Please answer asap with an explanation

Answer 1

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

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* breadth=length\ of AE*length\ of DE`

Area of ABDE =
`7*8=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 =
`(1)/(2)* base* height}=(1)/(2)* length\ of\ BD* length\ of\ GF`

Area of BCD =
`(1)/(2)*7*3=(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`.