Answer:
Therefore,
AD = 7 unit
AE = 600 unit
EF = 30 unit
FB = 5 unit
Ar(EFGH)= 210 unit²
Ar(ABCD)= 4445 unit²
Explanation:
Given:
Consider a rectangle ABCD as shown in the figure below where,
Area (ABCD) = 635 × 7 = 4445
Therefore length and width of a rectangle will be
LENGTH =635 = AB
WIDTH = 7 = AD
To Find:
AE =?
EF = ?
FB = ?
Ar(EFGH)=?
Ar(ABCD) =?
Solution:
We know that area of the rectangle is given by
![\textrm{Area of rectangle}= LENGTH* WIDTH](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5ffph9uirxnggrtu6j19qbcoc40jt1ztmh.png)
![\textrm{Area of rectangle ABCD}= 635* 7=4445\ unit^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/t5srzfs4n9hfev09z6yybfubhvr7zluv6i.png)
Substituting the values we get
![\textrm{Area of rectangle AEHD}= AE* 7\\\\4200=AE* 7\\\therefore AE=(4200)/(7)=600](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ne9qsdjiw2utwtrk3svos0rniqaf21pgc0.png)
Similarly for area rectangle FBCG,
![\textrm{Area of rectangle FBCG}= FB* 7\\\\35=FB* 7\\\therefore FB=(35)/(7)=5](https://img.qammunity.org/2021/formulas/mathematics/middle-school/he0n41zvu2g3fu0lhleyg71f1n9itlgda0.png)
Now we have
AB = 635,
![AE + EF + FB = 635\\\\600+EF+5=635\\\\EF=635 -605=30\\\therefore EF = 30](https://img.qammunity.org/2021/formulas/mathematics/middle-school/nkn6wndbww5g47c833bb6ggvx5wo2r1zpd.png)
Similarly for area rectangle EFGH,
![\textrm{Area of rectangle EFGH}= EF* 7\\\\=30* 7=210\ isunit^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/yupinnyhzvj9hb9ypkng03exbiibr292el.png)
Therefore,
AD = 7 unit
AE = 600 unit
EF = 30 unit
FB = 5 unit
Ar(EFGH)= 210 unit²
Ar(ABCD)= 4445 unit²