# Mensuration

1. The side of a square is 2cms less than the length of a rectangle and the breadth of the rectangle is 5 cms less than the side of the square.The area of the square is 324 sq.cms. What is the area of the Rectangle?

(a) 250 sq.cms

(b) 260 sq.cms

(c) 254 sq.cms

(d) 258 sq.cms

(e) None of these

Answer: (b)

Explanation:

Side of the square=√Area

=√324=18 cm

Length of the Rectangle=20 cm

Breadth=18-5=13cm

Area of the Rectangle = Length×Breadth

=20×13

=260 sq.cm

2. There is a circular ground whose area is 246400 sq.m . If a Person runs at the speed of 14.08 m/sec, then how much time will he take to complete the circle?

(a)125 sec

(b)130 sec

(c)100 sec

(d)120 sec

(e)None of these

Answer: (a)

Explanation:

If the radius of circular ground be r meter, then =246400 r =√78400=280 meter.

Circumference of the ground =2πr =1760 meter

Time taken = =125 seconds

3. One of the Angles of a Parallelogram is 45° . What will be the sum of the larger angle and twice the smaller angle of the Parallelogram?

(a) 228°

(b) 224°

(c) 225°

(d) 222°

(e) None of these

Answer: (c)

Explanation:

=180°-45°=135°

Required Value=135+2×45

=135+90

=225°

4. If the perimeter of a Rectangle is 180 meters and the difference between the length and the breadth is 8 meters, What is the area of the Rectangle?

(a) 2116 sq.mtr

(b) 2047 sq.mtr

(c) 2090 sq.mtr

(d)2178 sq.mtr

(e) None of these

Answer: (e)

Explanation:

Length = x meter

Breadth=(x-8)meter

2(x+x-8)=180

2x-8=90

X=49 meter

Breadth=49-8=41 meter

Area of the Rectangle =49×41 meter

=2009 meter.

5. The area of a rectangle is twice the area of the triangle . The Perimeter of the rectangle is 58 cm. What is the area of the triangle?

(a) 106

(b) 108

(c) 104

(d) Cannot be determined

(e ) None of these

Answer: (d)

Explanation:

According to the question,

Length+Breadth=29 cm

We don’t  know either length or breadth .

Hence , we cannot determined.

6. Radius of a circular garden is 7 meter more than length of a rectangle whose perimeter is 364 meter and breadth is 84 meter . What will be cost of fencing the garden (only at circumference),if the cost of fencing is Rs.8 per meter?

(a) Rs.5456

(b) Rs.6144

(c)Rs.5296

(d)Rs.5280

(e) None of these

Answer: (d)

Explanation:

2(l+b)=364

(l+b)=182

l+84=182

l=182-84=98 meter

Radius of circular Garden = 98+7=105 meter

Circumference of Garden= = =660 meter

Cost of fencing = 660×8

7. What would be the diagonal of a square whose area is 25 sq.cm?

(a)7

(b)√60

(c)9

(d)Cannot be determined

(e)None of these

Answer: (e)

Explanation:

Diagonal of square=√Area =√25=5 cm

8.What will be the area of a circle whose perimeter is 88 cms?

(a) 576

(b) 616

(c) 636

(d) cannot be determined

(e) None of these

Answer: (b)

Explanation:

Let the radius of circle be r cms  Area= 9. The area of a rectangle with 10 cm length is equal to the area of a circle . Find the circumference of the circle?

(a) 36 cm

(b) 34 cm

(c) 26 cm

(d) cannot be determined

(e) None of these

Answer: (d)

Explanation:

To find out the area of a rectangle we should know both the length and width of the rectangle. S0, we cannot be determined.

10.One angle of a right angle triangle is 35°. Which of the following is one of its angle?

(a)45

(b)60

(c)55

(d)Cannot be determined

(e)None of these

Answer: (c)

Explanation:

Third Angle= 180°-(90°+35°)

=55°