Chapter 3: How Many Squares?

Solution:-

The completed shape = 2 complete square + 4 half square

= 2 + (½ × 4)

= 2 + 2

= 4 cm²

Solution:-

Solution:-

Area of rectangle = 10 × 2

= 20 cm²

Then, the area of two equal triangles = 20/2

= 10 cm²

Because it is given that a straight line divides the rectangle into two equal triangles.

b) Draw one straight line in this rectangle to divide it into two equal rectangles. What is the area of each of the smaller rectangles?

Solution:-

Area of big rectangle = 10 cm²

The area of each of the smaller rectangles = 20/2

= 10 cm²

c) Draw two straight lines in this rectangle to divide it into one rectangle and two equal triangles.

Solution:-

(i) What is the area of the rectangle?

Solution:-

Area of rectangle = length × breadth

= 2 × 5

= 10 cm²

(ii) What is the area of each of the triangles?

Solution:-

Area of each triangle = ½ × area of the smaller rectangle

= ½ × 10

= 5 cm²

Solution:-

Using 5 squares, I can draw 12 shapes, as shown below:

b) Which shape has the longest perimeter? How much?

Solution:-

Shape 4 has the smallest perimeter out of the 12 shapes; the rest of the shapes have the same perimeter, i.e. = 1 + 1 + 1 + 1 + 1 + 1+ 1 + 1 + 1 + 1 + 1 + 1 = 12 cm

c) Which shape has the shortest perimeter? How much?

Solution:-

Out of 12 shapes, 4 have the smallest perimeter.

i.e. = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10 cm.

d) What is the area of the shapes (in square cm)?

Solution:-

There are 12 shapes, and each shape has five complete squares. The area of 1 square is equal to 1 cm².

So, the area of each shape = 1 × 5 = 5 cm²

Solution:-

By observing the given figure, shape C and shape D will tile a floor without any gaps.