Answer:
Question-6;
The value of [tex]x=7.5[/tex] [tex]in[/tex]
Question-7;
So the Answer is 'A'
Step-by-step explanation:
Question-6;
From the portion 'ABCD';
Given the area of rectangle 'ABCD' is [tex]30[/tex] [tex]in^{2}[/tex] , [tex]AD=4[/tex] [tex]in[/tex] and [tex]AD=x[/tex] [tex]in[/tex]
We have the formula to find the area of rectangle;
Area of rectangle 'ABCD'[tex]=AD\times DC[/tex]
[tex]30=4\times x[/tex]
[tex]x=\frac{30}{4}[/tex]
[tex]x=7.5[/tex] [tex]in[/tex]
So the value of [tex]x=7.5[/tex] [tex]in[/tex].
Question-7;
From figure;
Given;
All values [tex]AB=CD=FG=IJ=9[/tex] [tex]cm[/tex] , [tex]AC=BD=5[/tex] [tex]cm[/tex] , [tex]CF=DG=4[/tex] [tex]cm[/tex] , [tex]FI=GJ=3[/tex] [tex]cm[/tex] and [tex]EF=GH=3[/tex] [tex]cm[/tex]
In Rectangle 'ABIJ' have three sub-rectangle which are 'ABCD' , 'CDFG' and 'FGIJ'
Area of Rectangle 'ABIJ' equal to sum of area of Rectangle 'ABCD' , area of Rectangle 'CDFG' and area of Rectangle 'FGIJ'
Area of Rectangle 'ABIJ'[tex]=(AB\times AC)+(CD\times CF)+(FG\times FI)[/tex]
Plug all values in above equation,
Area of Rectangle 'ABIJ'[tex]=(9\times 5)+(9\times 4)+(9\times 3)[/tex]
Area of Rectangle 'ABIJ'[tex]=108[/tex] [tex]cm^{2}[/tex]
Also from figure;
[tex]\bigtriangleup CEF[/tex] and [tex]\bigtriangleup DGH[/tex] have same Area.
Total Area of this two triangle[tex]=2\times Area of \bigtriangleup CEF[/tex]
Total Area of this two triangle[tex]=2\times\frac{1}{2}\times BASE \times HIGHT[/tex]
Total Area of this two triangle[tex]=2\times\frac{1}{2}\times EF \times CF[/tex]
Plug 'EF' and 'CF' values in above equation,
Total Area of this two triangle[tex]=2\times \frac{1}{2} \times3 \times 4[/tex]
Total Area of this two triangle[tex]=12[/tex] [tex]cm^{2}[/tex]
∴ Total surface area of the building block is [tex](108+12)=120[/tex] [tex]cm^{2}[/tex]
