Mensuration

1 )

What will be the area of trapezium whose parallel sides are 22 cm and 16 cm long, and the distance between them is 11 cm?

209 cm2

282 cm2

265 cm2

179 cm2

302 cm2

View Solution

Answer :

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)

= 1/2 (22 + 16) * (11)

= 209 cm²

2 )

The perimeter of a rectangle is 42 m. If the area of the square formed on the diagonal of the rectangle as its side is 1 1/12 % more than the area of the rectangle, find the longer side of the rectangle.

19 m

16 m

9 m

5 m

12 m

View Solution

Answer :

Let the sides of the rectangle be l and b respectively.
From the given data,
√(l2 + b2) = (1 + 1 1/12) lb
=> l2 + b2 = (1 + 13/12) lb = 25/12 * lb
12(l² + b² ) = 25 lb
Adding 24 lb on both sides
12 l² + 12b² + 24lb = 25 lb
12(l² + b² + 2lb) = 49 lb
12(l + b)² = 49lb
but 2(l + b) = 42 => l + b = 21
So 12(21)² = 49lb
Solve, we get lb = 108
Since l + b = 21, longer side = 12 m3.

3 )

At the rate of Rs. 2 per sq m, cost of painting a rectangular floor is Rs 5760. If the length of the floor is 80% more than its breadth, then what is the length of the floor?

25 m

72 m

67 m

56 m

46 m

View Solution

Answer :

Let the length and the breadth of the floor be l m and b m respectively.

l = b + 80% of b = l + 0.8 b = 1.8b

Area of the floor = 5760/2 = 2880 sq m

l*b = 2880 i.e., l * l/1.8 = 2880

l = 72

4 )

A 7 m wide path is to be made around a circular garden having a diameter of 7 m. What will be the area of the path in square meter?

298

256

308

365

387

View Solution

Answer :

Area of the path = Area of the outer circle - Area of the inner circle

= π{7/2 + 7}2 - π [7/2]2

= 308 sq m

5 )

The perimeter of a rectangle of length 62 cm and breadth 50 cm is four times perimeter of a square. What will be the circumference of a semicircle whose diameter is equal to the side of the given square?

36 cm

25 cm

29 cm

17 cm

16 cm

View Solution

Answer :

Let the side of the square be a cm.

Parameter of the rectangle = 2(62 + 50) = 224 cm

Parameter of the square = 56 cm

i.e. 4a = 56

So a = 14

Diameter, d of the semicircle = 14 cm

Circumference of the semicircle = 1/2(π)(r) + d

= 1/2 * (22/7) * (7) + 14 = 25 cm

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