1.
A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Answer: Option 'B'
Given that area of the field = 680 sq. feet
=> lb = 680 sq. feet
Length(l) = 20 feet
=> 20 × b = 680
=> b = 680/20 = 34 feet
Required length of the fencing = l + 2b = 20 + (2 × 34) = 88 feet
2.
The area of the largest triangle that can be inscribed in a semicircle pf rasius r Cm, is:
Answer: Option 'C'
Area of the largest triangle = (1/2 × 2r × r) cm2 = r2 cm2
3.
A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:
Answer: Option 'D'
Distance covered in (9×1000)/(3600) × 12 = 30 m
Diagonal of squarre field = 30 m.
area of square field = 302/2
= 900/2 = 450 Sq.m
4.
A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
Answer: Option 'C'
Let the areas of the parts be x hectares and (900 - x) hectares.
Difference of the areas of the two parts = x - (900 - x) = 2x - 900
one-fifth of the average of the two areas = 1/5[x+(900−x)]/2
= 1/5 × (900/2) = 450/5 = 90
Given that difference of the areas of the two parts = one-fifth of the average of the two areas
=> 2x - 900 = 90
=> 2x = 990
⇒ x = 990/2 = 495
Hence, area of smaller part = (900 - x) = (900 – 495) = 405 hectares.
5.
The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:
Answer: Option 'D'
Radius of required circle = 14 Cm
its area = 22/7 × 14 × 14
44 × 14 = 616 Cm2