Changing Boundaries

Q. A square of side 2 cm is cut out from a corner of a square of side 4 cm. What is the perimeter of the resulting figure?

1. 18 cm
2. 20 cm
3. 16 cm
4. 12 cm

Q. A square of side 1 cm is cut out from a corner of the below given rectangle. What is the perimeter of the resulting figure?

1. 12 cm
2. 10 cm
3. 8 cm
4. 16 cm

Q. A square of boundary 64 cm is given to us. If we remove a square of side 2 cm from one corner of the bigger square, the length of the new boundary ___.

1. increases
2. decreases
3. cannot be determined
4. remains the same

Q. We cut out squares(white) of side 10 cm from a square of side 40 cm. Match the new shapes to their perimeters.

1. 160 cm
2. 200 cm
3. 180 cm

Q. The king wishes to remove his portrait from the photo frame. Calculate the area of the frame of the photograph to be removed from the figure below.

1. 600 sq. in.
2. 1200 sq. in.
3. 750 sq. in.
4. 1000 sq. in.

Q.

A wire is cut into several small pieces. Each of the small pieces is bent into a square of side $2$ cm. If the total area of the small squares is $28$ square cm, what was the original length of the wire?

Q. We cut out squares(white) of side 10 cm from a square of side 40 cm. Match the new shapes to their perimeters.

1. 160 cm
2. 200 cm
3. 180 cm

Q. The border of an equilateral triangle of side 4 cm is covered using a ribbon of a given length. What would be the side of a square if the same ribbon covers its boundary completely?

1. 5 cm
2. 3 cm
3. 4 cm
4. 6 cm

Q. If we remove a square of side 2 cm from each corner of a square frame of side 8 cm, then the perimeter of the resulting shape is .

1. 40 cm
2. 32 cm
3. 30 cm
4. 20 cm

Q.

Avneet buys$ 9$ square paving slabs, each with a side of $ \frac{1 }{2}$ m. He lays them in the form of a square.

(a) What is the perimeter of his arrangement $ \text{[fig 10.7(i)]}$?

(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement $ \text{[(Fig 10.7 (ii)]}$?

(c) Which has a greater perimeter?

(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this?

(The paving slabs must meet along complete edges i.e they cannot be broken.)

(i) (ii)

Q. A square of side 1 cm is cut out from a corner of the below given rectangle. What is the perimeter of the resulting figure?

1. 16 cm
2. 8 cm
3. 12 cm
4. 10 cm

Q. When a square is cut out from all four corners of a larger square, the perimeter of the resulting figure is greater than the larger square.

1. True
2. False

Q. 4 squares each of side 1 cm are cut out from a square of side 4 cm. The length of the boundary of the resulting shape is ___.

1. 12 cm
2. 9 cm
3. 16 cm
4. 20 cm

Q. We cut out squares(white) of side 10 cm from a square of side 40 cm. Match the new shapes to their perimeters.

1. 160 cm
2. 200 cm
3. 180 cm

Q. From the corner of the given square of side length of 10 cm, a small square of side 1 cm is cut off. What will be its new perimeter (in cm)?

1. 30
2. 38
3. 36
4. 40