Chapter 9: Perimeter and Area

Solution:-

1 cm² = 100 mm².

We know that, 1 cm = 10 mm

1 cm² = 10² mm²

Solution:-

1 hectare = 10,000 m²

Solution:-

Area of a triangle = ½ × base × height.

Solution: –

1 km² = 10,00,000 m².

We know that, 1 km = 1000 m

1 km² = 1000² m²

Solution:-

Area of a square of side 6 m is equal to the area of 3,60,000 squares of each side 1 cm.

Let us assume the number of squares having side of 1 cm be ‘x’.

As per the condition in the question,

Area of the side 6 m square = Area of side 1 cm square

(6m)² = x(1cm)²

360000 cm² = x cm² … [because 1 m = 100 cm]

x = 360000cm²/1 cm²

x = 360000

Solution:-

10 cm² = 0.001 m².

We know that, 1 m = 100 cm

1 m² = 10000 cm²

10 cm² = 10/10000

= 0.001 m²

In Questions 57 to 72, state whether the statements are True or False.

Solution:-

True.

Perimeter of a closed figure is the distance around it while area is the measure of the part of plane or region enclosed by it.

Hence, perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i).

Solution:-

True.

By observing the figure, we can say that area of both figures are same, because number of blocks used in both figures are same.

(b) Perimeter of (ii) is the same as (i).

Solution:-

False.

By observing the figures, we can say that there are 2 new sides added in figure (ii).

Therefore, the perimeter of (ii) is not same as (i).

(c) If (ii) is divided into squares of unit length, then its area is 13 unit squares.

Solution:-

False.

We know that, area of square = side × side

Then area of 1 square = 1 × 1

= 1 unit squares

There are 12 squares in figure (ii).

Therefore, area of figure (ii) = 12 × 1 = 12 unit squares

(d) Perimeter of (ii) is 18 units.

Solution:-

True.

The perimeter refers to the total length of the sides or edges of a polygon.

Solution:-

False.

Solution:-

True.

We know that congruent triangles have equal sizes and shapes.