Answer:

The length of each side of red square is 1 cm.

• We can make 7 rectangles as shown in the figure.
• The rectangle 1 and rectangle 2 has the longest perimeter.
• The rectangle 3, rectangle 4, rectangle 5 and rectangle 6 has the smallest perimeter.

Answer:

(a)
Stamp A covers 18 squares, each of one centimetre side. Stamp B covers 8 squares each of 1 centimetre side.

(b)
Stamp A has the biggest area.
Stamp A covers 18 squares, each of one centimetre side.
Area of biggest stamp = 18 square cm

(c)
Stamp D and stamp F has same area.
Stamp D and stamp F covers equal number of squares. Each of them covers 12 squares of one centimetre side.
Area of each of these stamps = 12 square cm

(d)
Stamp E is the smallest stamp. It covers 4 squares, each of one centimetre side.
Area of smallest stamp = 4 square cm
Now, area of biggest stamp = 18 square cm
Difference between the area of smallest stamp and biggest stamp = (18 – 4) square cm
= 14 square cm

Answer:

(a)
The pages of this book has a larger area than the footprint.

(b)
A hundred rupee note has smaller area than two five-rupees notes kept
together.

(c)
The area of a 10 rupee note is less than 100 square cm.

(d)
The yellow and blue shaped figures are divided into 2 triangles of equal areas. We now see that the area of each triangle of the blue shape is more than the area of each triangle of the yellow shape. We can then say, that the area of the blue shape is more than the area of the yellow shape.

(e)
With the help of a ruler, we come to find that the length of the boundary of the blue shape is more than the length of the boundary of the yellow shape. Thus, we can say that the perimeter of the blue shape is greater than that of the yellow shape.

Answer:

We will trace the hand on the paper and find the area of the paper that gets covered by hand with the help of a square of side 1 cm.

Disclaimer: Students are advised to prepare the answer on their own.

Answer:

We will ignore a square if it is less than half-filled but we will count the square as 1, if it is more than half-filled.

Figure A covers three squares that are more than half-filled, three squares that are less than half-filled, and three complete squares.

We know that an area of one complete square = 1 square cm
Area of figure A = area of three more than half-filled squares + area of three complete squares
= (3 + 3) square cm
= 6 square cm

Figure B covers four complete squares, eight squares that are half-filled, and four squares that are less than half-filled.
Area of figure B = area of four complete squares + area of eight half filled squares
= (4 + 4) square cm
= 8 square cm

Figure C covers two complete squares, two squares that are more than half-filled, and two squares that are less than half-filled.
Area of figure C = area of two complete squares + area of two squares more than half-filled
= (2 + 2) square cm
= 4 square cm

Figure D covers five complete squares and two squares that are half-filled.
Area of figure D = area of five complete squares + area of two half-filled squares
= (5 + 1) square cm
= 6 square cm

Figure E covers 18 complete squares and six squares that are half-filled.
Area of figure E = area of 18 complete squares + area of six half filled squares
= (18 + 3) square cm
= 21 square cm

Figure F covers four squares that are more than half-filled, four squares that are less than half-filled, and four complete squares.
Area of figure F = area of four squares more than half-filled squares + area of four        complete  squares
= (4 + 4) square cm
= 8 square cm

Answer:

Area of big rectangle = 20 square cm
Now, it is given that area of blue triangle is half the area of a big rectangle.
Area of blue triangle = (20 ÷ 2) square cm
= 10 square cm

Answer:

There are two rectangles. The orange rectangle contains 12 complete squares and the green rectangle contains 8 complete squares.

Thus, area of an orange rectangle = 12 square cm

Area of green rectangle = 8 square cm
Area of the orange portion of a triangle = (12 ÷ 2) square cm
= 6 square cm

Area of green portion of the triangle = (8 ÷ 2) square cm
= 4 square cm
Area of red triangle = (6 + 4) square cm
= 10 square cm

So, the area of red triangle is 10 square cm.

Answer:

• Yes, Asif is correct.

• We will ignore a square that is less than half-filled, and we will count the square as 1, if it is  more than half-filled.

In the green portion, we have two complete squares and four half squares.

Area of one complete square    = 1 square  cm
So, total area of green portion = area of two complete squares + area of four half squares
= (2 + 2) square cm
= 4 square cm

In the yellow portion, we have three complete squares, three squares that are more than half-filled, and two squares that are less than half-filled.

Now, area of 1 complete square = 1 square cm

Area of the yellow portion = area of three complete squares + area of three squares more than half-filled
= (3 + 3) square cm
= 6 square cm

Answer:

Answer:

The given figure comprises of 2 half-filled squares and 2 squares that are less than half-filled. Thus, we will ignore the squares that are less than half filled.

So, area of the given figure = 1 square cm

Therefore, it clearly proves that the area of the figure i.e. 1 square cm is less than 2 square cm.

Answer:

(a)
The given rectangle is divided into two equal triangles by drawing a line as shown below.

Area of rectangle       = 20 square cm
Area of each triangle =

12of area of rectangle
= (20 ÷ 2) square cm
= 10 square cm

(b)
The given rectangle is divided into two equal rectangles by drawing a line as shown below.

Area of rectangle = 20 square cm
Thus, area of each small rectangle =

12of area of rectangle
= (20 ÷ 2) square cm
= 10 square cm

(c)
The given rectangle is divided into one rectangle and two equal triangles by drawing 2 lines as shown below.

We will consider a square as complete if it is more than half-filled, and will ignore a square if it is less than half-filled.

Thus, in the red shaded region, we have 2 completely filled squares and 2 squares that are more than half-filled.
Thus, the area of red triangle = 4 square cm

Similarly, the area of green triangle = 4 square cm
Now, the area of remaining portion i.e. the rectangle contains 12 completely filled squares.

• Thus, the area of rectangle = 12 square cm.
• Area of each of the triangle is 4 square cm.

Disclaimer: The answer to part (c) of the question may vary from student to student. The answer provided here is for reference only.

Answer:

(a)
There are 12 different shapes that can be drawn using 5 squares.

(b)
Among all the 12 shapes, there is only one shape, figure (d) that has the smallest perimeter, but all the other shapes have same and longest perimeter.

Longest perimeter of each 11 shapes = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) cm
= 12 cm

(c)
The figure (d) has the smallest perimeter.
Perimeter of figure (d) = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) cm
= 10 cm

(d)
We find that each of the 12 shapes covers 5 complete squares.
Area of 1 complete square   = 1 square cm
Area of 5 complete squares = 1 × 5 square cm
= 5 square cm

Area of each shape = Area of 5 complete squares
= 5 square cm

Answer:

The shapes C and D will tile a floor without leaving any gaps.
Area of each shape = 2 × 2
= 4 square cm

Design with shape C

Design with shape D

Disclaimer: The answer may vary from student to student. It is highly recommended that the students prepare the answer on their own.