S.chand publication New Learning Composite mathematics solution of class 8 Chapter 11 Representing 3D Shapes in 2D Exercise 11A

 Exercise 11A

Question 1

Sol :

(a)

h=6cm , a=8cm ,b=11cm

Area $=\frac{1}{2}\times h (a+b)$

$=\frac{1}{2}\times 6(8+11)$

$=\frac{1}{2}\times 6 \times 19$

=57cm²

(b)

h=10cm, a=12cm, b=9cm

Area$=\frac{1}{2}h(a+b)$

$=\frac{1}{2}\times 10(12+9)$

=5×21=105cm²

(c)

h=4cm, a=3cm, b=5cm

Area$=\frac{1}{2}h(a+b)=\frac{1}{2}\times 4 (3+5)$

=2×8=16cm²

Question 2

Sol :

Area=80cm²

a=9cm

b=7cm

∴We know

Area$=\frac{1}{2}h(a+b)$

$80=\frac{1}{2}h(9+7)$

$h=\frac{80\times 2}{16}=10$ cm

Question 3

Sol :

a+b=25cm

Area=150cm²

We know that-

Area$=\frac{1}{2}h(a+b)$

$h=\frac{area \times 2}{25}=\frac{150\times }{25}$

=12cm

Question 4

Sol :

Area=126cm²

h=6cm

a+b=?

We know that-

Area$=\frac{1}{2}h(a+b)$

$a+b=\frac{126\times 2}{6}$

a+b=42

Question 7

Sol :

Let , a=x

b=x-20

h=22 m

Area=450m²

We know that

$\frac{1}{2}\times h(a+b)=450$

$\frac{1}{2}\times 15 (x+x-20)=450$

$2x-20=\frac{450\times 2}{15}$

2x=60+20=80

$x=\frac{80}{2}40$

∴a=40m

b=40-20=20m

Question 8

Sol :

Let , common factor be x

a=7x , b=9x

Area=960cm²

h=15cm

According to question

Area$=\frac{1}{2}h(a+b)$

$960=\frac{1}{2}\times 15(7x+9x)$

$16x=\frac{960\times 2}{15}$

$x=\frac{64\times 2}{16}$=8

∴a=7×8=56cm

b=9×8=72cm

Question 9

Sol :

a=10cm =AB

b=20cm=CD

AD=BC=13cm

AD||BQ  ∴AD=BQ=13cm

AB||DB  ∴AB=DQ=15cm

∴QC=DC-DQ=20-10=10cm

∵BO bisects QC

∴QO=OC$=\frac{10}{2}=5$cm

∴h²=BO²=BC²-OC²

=13²-5²

=169-25=144

h=√144=12

∴$A=\frac{1}{2}h(a+b)$

$=\frac{1}{2}\times 12 (10+20)$

=6×30=180cm²

Question 10

Sol :

AB=15cm

DC=31cm

AD=BC=17cm

AD||BE  ∴AD=BE=17cm

AD=BE=17cm

∴EC=DC-DE=31-15=16cm

∴OC=EO$=\frac{16}{2}=8$cm

∴ΔBOC-

BO²=BC²-OC²

=17²-8²

=289-64=225

BO=√225=15

∴BO=h=15cm

Area$=\frac{1}{2}h(a+b)$

$=\frac{1}{2}\times 15(31+15)$

$=\frac{1}{2}\times 15 \times 46$

=343cm²

Question 11

Sol :

h=16m

a=20m

b=25m

$A=\frac{1}{2}\times h(a+b)$

$=\frac{1}{2}\times 16(20+25)$

=8×45=360m²

∴Area of floor=360m²

Rate=40 per m²

∴Cost=360×40=14400