Chapter 9: Perimeter and Area

Solution:-

(b) 200 cm²

From the question, it is given that, radius of circle 10 cm.

Square has diagonal equal to its diameter.

Diameter = 2 × radius

= 2 × 10

= 20 cm

Then, let us assume the side of the square be P.

So, area of square be P².

By the rule of the Pythagoras theorem,

Diagonal² = height² + base²

20² = P² + P²

20² = 2P²

400 = 2P²

P² = 400/2

P² = 200 cm²

Therefore, the area of the largest square that can be cut out of a circle of radius 10 cm is 200cm².

Solution:-

(a) 4 cm

From the question, it is given that, the largest circle can be cut out of the rectangle measuring 10 cm in length and 8 cm in breadth.

Diameter of circle = 8 cm

Then, radius = diameter/2

= 8/2

= 4 cm

Solution:-

(a) 60 cm

Perimeter of the given figure = AB + BC + CD + DE + EF + FG + GH + IH + IJ + AJ

= (AJ + IH + GF + BC = DE) + 3 + 5 + 2 + 20 + 4 + 6

= 20 + 40

= 60 cm

Solution:-

(b) 18πr

Let us assume R be the radius of circle

We know that, area of circle = πR²

81πr² = πR²

R = √81 r

R = 9r

Circumference = 2 πR

= 2 π (9r)

= 18πr

Solution: –

(b) 10 π

Let us assume the side of the square be x.

From the question, it is given that, area of a square is 100 cm²

We know that, area of square = 100 cm²

x² = 100 cm²

x = √100 cm²

x = 10 cm

So, for the largest circle in the square, diameter of the circle must be equal to the side of the square.

Diameter = 10 cm = side of square

2r = 10 cm

r = 10/2

r = 5 cm

then, circumference of circle = 2 πr

= 2 × π × 5

= 10 π

Solution:-

(a) 9 times

Area of circle = πr²

From the question, the radius of a circle is tripled = 3r

Then, area = π(3r)²

= 9πr²

Solution:-

(a) 8πr²

We know that, area of semicircle = πr²/2

Then, the area of a semicircle of radius 4r is = (π(4r)²)/2

= 16πr²/2

= 8πr²

In Questions 38 to 56, fill in the blanks to make the statements true.

Solution:-

Perimeter of a regular polygon = length of one side × (number of sides)

Solution:-

If a wire in the shape of a square is rebent into a rectangle, then the perimeter of both shapes remain same, but area may vary.

Solution:-

Area of the square MNOP of Fig. 9.24 is 144 cm². Area of each triangle is 18cm².

From the question it is given that, Area of the square MNOP is 144 cm².

Then, area of triangle = (1/8) × Area of the square MNOP

= 1/8 × 144

= 18 cm²