Question 1

The area of a rhombus having one side 10 cm and one diagonal 12 cm is

Accepted Answer

96 cm2

Question 2

The cost of levelling a circular field at 50 Paise per square metre is Rs 7700. The cost (in Rs) of putting up a fence all round it at Rs 1.20 per meter is ( Use π = 22/7)

Accepted Answer

Rs 528

Question 3

From the four corners of a rectangular sheet of dimensions 25 cm x 20 cm, square of side 2 cm is cut off from four corners and a box is made. The volume of the box is

Accepted Answer

1000 cm3

Question 4

The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in cm2 is

Accepted Answer

20

Question 5

The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circum circle and the incircle of the triangle is (use: π = 22/7)

Accepted Answer

50 2/7 sq.cm

Question 6

If each side of a square is increased by 25%, find the percentage change in its area?

Accepted Answer

let each side of the square be a , then area = a 2 As given that The side is increased by 25%, then New side = 125a/100 = 5a/4 New area = 5 a 4 2 Increased area= 25 a 2 16 - a 2 Increase %= 9 a 2 / 16 a 2 * 100 % = 56.25%

Question 7

If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.

Accepted Answer

let length = x and breadth = y then 2(x+y) = 46 => x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² => x²+y²+2xy= 529 => 289+ 2xy = 529 => xy = 120 area = xy = 120 sq.cm

Question 8

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

Accepted Answer

Let original radius = R. New radius = 50 100 R = 50 100 R Original area = R 2 and new area = πR 2 3 πR 2 4 * 1 πR 2 * 100 Decrease in area = π R 2 2 = πR 2 4 = 75%

Question 9

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

Accepted Answer

l 2 + b 2 = 41 (or) l 2 + b 2 = 41 Also, l b = 20 l + b 2 = l 2 + b 2 + 2 l b = 41 + 40 = 81 (l + b) = 9. Perimeter = 2(l + b) = 18 cm.

Question 10

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

Accepted Answer

let ABCD be the given parallelogram area of parallelogram ABCD = 2 x (area of triangle ABC) now a = 30m, b = 14m and c = 40m s=1/2 x (30+14+40) = 42 Area of triangle ABC = s s - a s - b s - c = 42 12 28 2 = 168sq m area of parallelogram ABCD = 2 x 168 = 336 sq m

Question 11

The percentage increase in the area of a rectangle, if each of its sides is increased by 20%

Accepted Answer

Let original length = x metres and original breadth = y metres. Original area = xy sq.m Increased length = 120 100 and Increased breadth = 120 100 New area = 120 100 x * 120 100 y = 36 25 x y m 2 The difference between the Original area and New area is: 36 25 x y - x y 11 25 x y Increase % = 11 25 x y x y * 100 = 44%

Question 12

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

Accepted Answer

Let the side of the square(ABCD) be x meters. Then, AB + BC = 2x metres. AC = 2 x = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = 0 . 59 x 2 x * 100 = 30% (approx)

Question 13

Find the ratio of the areas of the incircle and circumcircle of a square.

Accepted Answer

Let the side of the square be x. Then, its diagonal = 2 x 2 = 2 x Radius of incircle = x 2 Radius of circum circle= 2 × x 2 = x 2 Required ratio = πx 2 4 : πx 2 2 = 1 4 : 1 2 = 1 : 2

Question 14

A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be

Accepted Answer

length of wire = 2 πr = 2 x (22/7 ) x 56 = 352 cm side of the square = 352/4 = 88cm area of the square = 88 x 88 = 7744sq cm

Question 15

The ratio of the area of a square to that of the square drawn on its diagonal is

Accepted Answer

ratio = a 2 2 a 2

Question 16

The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is

Accepted Answer

The diameter is equal to the shortest side of the rectangle. So radius= 14/2 = 7cm. Therefore, a r e a o f c i r c l e = πr 2 = 22 7 × 49 = 154 cm 2

Question 17

One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

Accepted Answer

Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m

Question 18

The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32cm. Find the area of the triangle?

Accepted Answer

let ABC be the isosceles triangle, the AD be the altitude Let AB = AC = x then BC= 32-2x [because parameter = 2 (side) + Base] since in an isoceles triange the altitude bisects the base so BD = DC = 16-x In a triangle ADC, A C 2 = A D 2 + D C 2 x 2 = 8 2 + 16 - x 2 ⇒ x = 10 BC = 32-2x = 32-20 = 12 cm Hence, required area = 1 2 * B C * A D = 1 2 * 12 * 10 = 60 sq cm

Question 19

If the length of the diagonal of a square is 20cm,then its perimeter must be a. 402 cm b. 302 cm c. 10cm d. 15 2 cm

Accepted Answer

We know that d=√2s Given diagonal = 20 cm => s = 20/ 2 cm Therefore, perimeter of the square is 4s = 4 x 20/ 2 = 40 2 cm.

Question 20

The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is

Accepted Answer

Let breadth = x m Then, length = (x+5)m Area of a rectangle = Length x Breadth x(x+5) = 750 x² + 5x - 750= 0 (x+30)(x-25)= 0 x = 25 or x = -30 Hence, breadth x = 25m => Length = x + 5 = 25 + 5 = 30m.

Area Questions