Chapter 9: Perimeter and Area

Solution:-

(b) 51.4 cm

From the question, it is given that, radius of semicircular disc 10 cm

We know that, perimeter of semicircular disc = circumference of semicircle + diameter

Circumference of semicircle = 2πr/2

= πr

= (22/7) × 10

= 31.4 cm

Then, total tape required = 31.4 + 10 + 10

= 51.4 cm

Solution:-

(c) 50.24 m²

We know that, area of circle = πr²

Diameter = 8m

Then, radius = 8m/2

Radius = 4 m

So, area = (22/7) × 4 × 4

= 50.24 m²

Solution:-

(d) πn²

We know that, area of circle = πr²

Where r = radius = n

Solution:-

(a) 3.08 m²

From the question it is given that, diameter of semicircular shape = 2.8 m

So, radius of semicircular shape = 2.8/2 = 1.4 m

Then, area of semicircular shape of table top = πr²/2

= ((22/7) × 1.4 × 1.4)/2

= 3.08 m²

Solution:-

(d) 1000000

We know that, 1 m = 100 cm

1 cm = 10 mm

So, 1 m = 10 × 100

1 m = 1000 mm

Then, 1 m² = 1000 × 1000

1 m² = 1000000

Solution:-

From the question, it is given that, if p squares of each side 1mm makes a square of side 1cm.

We know that, area of square of side 1mm = side × side

= 1 × 1

= 1 mm²

Then, area of square of side 1cm = side × side

= 1 × 1

= 1 cm²

So, area of square of side 1mm = area of square of side 1cm

P × 1 mm² = 1 cm²

Pmm² = (10mm)²

Therefore, Pmm² = 100 mm²

Solution:-

(b) 12 squares with side 1m each

Area of square = side × side

Area of square of 1 m side = 1 × 1

= 1 m²

Therefore, area of 12 squares of 1 m side = 12 × 1

= 12 m²

Solution:-

(b) 2 times

Consider b as the side and h as the height of a rhombus.

Area of rhombus = b x h                 [Since, area of rhombus = base x corresponding height]

Here, if each side of rhombus is doubled, then the side of rhombus = 2b

Area of rhombus = 2b x h = 2(b x h) = 2 times of original

Hence, if each side of a rhombus is doubled, its area will be increased by 2 times.

Solution:-

(b) 2 times

We know that, perimeter of parallelogram = 2 (length + breadth)

If the sides of a parallelogram are increased to twice its original lengths,

= 2 (2length + 2breadth)

= 2 × 2 (length + breadth)

Hence, the perimeter will increase by 2 times the perimeter of the original parallelogram.

Solution:-

(d) 4 times

We know that, area of the circle = πr²

Where, r = radius of original circle

Then, radius is doubled = 2r

Then, area of new circle = π(2r)²

= π4r²

Hence, the area will increase by 4 times the area of the original circle.