Question 1

if the side of a square be increased by 4 cms. The area increased by 60 sq. cms . The side of the square is?

Accepted Answer

Let each side = x cm Then, (x + 4 )2 - x2 = 60 ⇒ x 2 + 8x + 16 - x2 = 60 ∴ x = 5.5 cm

Question 2

A veranda 40 meters long 15 meters broad is to paved with stones each measuring 6 dm by 5 dm. the number of stones required is?

Accepted Answer

Length = (40 x 10 ) dm = 400 dm. Breadth = (15 x 10 ) dm = 150 dm. Area of veranda = (400 x 150 ) dm2 Area of one stone = (6 x 5 ) dm2 ∴ Required number of stones = (400 x 150) /(6 x 5) = 2000

Question 3

The length of a rectangular plot is twice of its width. If the length of a diagonal is 9√5 meters, the perimeter of the rectangular is?

Accepted Answer

Let breadth = y meters, Then, length = 2y meters ∴ Diagonal = √y2 + (2y)2 = √5y2 meters So, √5y2 = 9 √5 ∴ y= 9 Thus, breadth = 9 m and length = 18 m ∴ Perimeter = 2 (18 + 9) m = 54m.

Question 4

The length and breadth of a playground are 36 m and 21 m respectively. Flagstaffs are required to be fixed on all along the boundary at a distance of 3 m apart. The number of flagstaffs will be?

Accepted Answer

Perimeter = 2 x (36 + 21 ) m = 144 m ∴ Number of flagstaffs = 144 / 3 = 38

Question 5

If the length of diagonal AC of a square ABCD is 5.2 cm then area of the square ABCD is?

Accepted Answer

Area = 1/2 x (Diagonal)2 = (1/2) x 5.2 x 5.2 cm2 = 13.52 cm2

Question 6

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and the breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm 2 . Therefore , the length of the rectangle is?

Accepted Answer

Let breadth = b, length = 2b ∴ Area of rectangle = 2b x b = 2b2 As per question. ∵ (2b - 5 ) (b + 5 ) = 2b2 + 75 ⇒ 5b = 75 + 25 ⇒ 5b = 100 ∴ b = 100 / 5 = 20 Hence, length of the rectangle =2b = 2 x 20 = 40 cm.

Question 7

A park of 10 meters long and 8 meters broad. What is the length of the longest pole that can be placed in the park?

Accepted Answer

Length of the longest pole = √ [(10)2 + (8)2] m = √ 164 m = 12.8 m

Question 8

The ratio of the area of two square, one having and double its diagonal than the other is?

Accepted Answer

Let the diagonal of one square be (2d) cm Then, diagonal of another square = d cm ∴ Area of first square = [ 1/2 x (2d)2] cm2 Area of second square = (1/2 x d2) cm2 ∴ Ratio of area = (2d)2/ d2 = 4/1 = 4: 1

Question 9

If the diameters of a circle is increased by 100% . Its area is increased by?

Accepted Answer

Original area = π(d/2)2 = (πd2) / 4 New area = π(2d/2)2 = πd2 Increase in area = (πd2 - πd2/4) = 3πd2/4 ∴ Required increase percent = [(3πd2)/4 x 4/(πd2) x 100]% = 300%

Question 10

The ratio of the area of square of side a and equilateral triangle of side a is?

Accepted Answer

Ratio of area = a2/ √(3/4) a2 = 4/√3 = 4:√3

Question 11

The length of each side of an equilateral triangle having an area of 4√3 cm 2 is?

Accepted Answer

Area of equilateral triangle = √3/4 a2 = 4√3. ⇒ a2 = 16 ∴ a = 4 cm

Question 12

The area of an equilateral triangle whose side is 8 cms is?

Accepted Answer

Req. Area = √3/4 x a2 = √3/4 x 82 cm2 = 16√3 cm2

Question 13

Find the area of a triangle whose sides measure 8 cm, 10 cm and 12 cm.

Accepted Answer

Given that, a = 8 cm, b = 10 cm and c = 12 cm We know, that s = (a + b + c)/2 = (8 + 10 + 12)/2 = 30/2 = 15 cm ∴ (s - a) = (15 - 8) = 7 cm (s - b) = (15 - 10) = 5 cm (s - c) = (15 - 12) = 3 cm ∴ Area = √s(s - a) (s - b) (s - c) = √15 x 7 x 5 x 3 = √1575 = √25 x 63 = 5√63 cm

Question 14

Find the perimeter of a triangle with sides equal to 6 cm, 4 cm and 5 cm.

Accepted Answer

Given that, a = 6 cm, b = 4 cm and c = 5 cm Required perimeter = a + b + c = 6 + 4 + 5 cm = 15 cm

Question 15

The area of a right angled triangle is 40 sq cm. If its base is equal to 28 cm. find its height.

Accepted Answer

Given that, area = 40 sq cm, base = 28 cm and height = perpendicular = ? Area = (base x perpendicular) / 2 ⇒ 40 = (28 x perpendicular) / 2 ∴ perpendicular = 40/14 = 20/7 = 26/7 cm

Question 16

The area of a right angled triangle is 10 sq cm. If its perpendicular is equal to 20 cm, find its base.

Accepted Answer

Given that, area = 10 sq cm, perpendicular = 20 cm and base = ? area = (base x Perpendicular) / 2 ⇒ 10 = (base x 20) / 2 ∴ base = 1 cm

Question 17

One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?

Accepted Answer

Area of parallelogram = Base x Height = 8.06 x 2.08 = 16.76 cm2

Question 18

Find the area of a rectangle having 15m length and 8m breadth.

Accepted Answer

Required area = Length x Breadth = 15 x 8 = 120 sq m

Question 19

The length of a rectangular field is 100 m and its breadth is 40 m. What will be the area of the field?

Accepted Answer

Required area = Length x Breadth = 100 x 40 = 4000 sq m = 4 x 103 sq m

Question 20

If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.

Accepted Answer

According to the formula, Percentage increase in diagonals = 5%

Area Questions