InfyTQ Geometry Quiz 1

1dm=0.1m
Thus 19m2.5dm=19.25 & 12m5dm=12.5m
Area of path with overlapping = (19.25m X 2m) + (12.50m X 2m) = 63.5 m^{2}
Since area of path is overlapped which is shaded in below figure. So, subtract 2m x 2m =4 m^{2}
Hence, the actual area of path = (63.5 m^{2} – 4 m^{2}) = 59.5 m^{2}(Answer)

 



Video solution:

we know s=\frac{a + b + c}{2}
here a=6cm, b=8cm , c=12cm
therefore s=\frac{6 + 8 + 12}{2}
=26/2
=13
area of tringle=\sqrt{s(s-a)(s-b)(s-c)}
=\sqrt{13(13-6)(13-8)(13-12)}
=\sqrt{13\times 7\times 5\times 1}
=\sqrt{455}
=21.33(ans) [Here sqrt stands for square root]

Video Explanation:

2(a+b) = 18

(a+b)=9

√ (a² + b² ) = √41

Squaring on both sides

we have a² + b² = 41 and (a+b)² = 81

substituting the above values in the equation below

(a+b)² = a²+b² + 2ab

81 = 41 + 2ab

ab=20

Video Explanation:

Formula for rombus area is \frac{d_{1}\times d_{2}}{2} thus

\frac{8\times 10}{2} = 40 cm²

Video Explanation:

Required area = 2\sqrt{s(s-a)(s-b)(s-D)}

Where, S = \frac{a+b+D}{2} = \frac{5+4+7}{2} = 8

= 2\sqrt{8(8-5)(8-4)(8-7)}

= 2\sqrt{8\times 3\times 4} = 8√6 = 19.6 sqcm

area of rectangular plot = 112*78
=8736 m²
it has gravel path so, length = 112-2.5-2.5
=107m
breath = 78-2.5-2.5=73m
l*b= 107*73
=7811m²
area of path = 8736-7811
=925m²

Video Explanation:

Volume of a sphere = (4/3) * π * r³ --(1) ( here r =3cm)
Volume of circular plate of thickness 1 cm is = π * r² * h -- (2)
( here h=1 cm that is thickness )
Equating (1) and (2)
r=6cm

Answer:

The number so sides of the polygon are 14.

Solution :

The number of diagonals beingd=\frac{n(n-3)}{2}

where, n is the number of sides.

77={n(n-3)}{2}

154=n(n-3)

n²-3n-154=0

n²-3n-154=0

n²-14n+11n-154=0

n(n-14)+11(n-14)=0

(n-14)(n+11)=0

n=-11,14

Reject n=-11 and Accept n=14

Therefore, The number so sides of the polygon is 14.

Video Explanation:

2990.4 m
Solution: let a is side of square field then a²=31684
a=178
perimeter= 4 x a = 712
5% more than perimeter = 712 + 5% of 712 = 712 + 35.6 = 747.6
Because we enclose four times so 4 x 747.6 = 2990.4

the volume of a hollow cylinder=π * h* (R²-r²)
22/7 * 21m * (36-25)m^2
=66 * 11m³
=726 m³

Video Explanation: