**Hint:** Give example(s) in order to define perimeter of closed figures.

**Question.1.** Jatin is finding the perimeter of a figure. Which of these could be the figure?

(a) (b) (c) (d)

**Question.2.** In which of these situations will perimeter be calculated?

(a) Length of lace border needed to put around a rectangular table cover.

(b) Length of rope required to fence three sides of a rectangular backyard.

(c) Amount of water needed to fill a container.

(d) Amount of paint required to paint a wall.

**Ans.1.** (d) **Ans.2.** (a) Length of lace border needed to put around a rectangular table cover.

**Hint:** Deduce and apply the formula to determine the perimeter of a rectangle.

**Question.3.** Aditi wants to put decorative tape around the borders of a rectangular cardboard which is 50 cm long and 45 cm wide. Which of these expressions represents the length of tape, in cm, required to cover its borders?

(a) (50 × 45)

(b) (50 + 45)

(c) 2(50 × 45)

(d) 2(50 + 45)

**Question.4.** A student has to form distinct rectangles by using coloured ribbon and paste it on a sheet. If she uses 20 centimetres of ribbon for each rectangle, how many distinct rectangles she can form of dimensions of positive integers?

(a) 1

(b) 5

(c) 6

(d) 10

**Ans.3.** (d) 2(50 + 45)**Ans.4.** (b) 5

**Hint:** Deduce and apply the formula to determine the perimeter of a square.

**Question.5.** Arjun wants to fence his square backyard of side length 11 m using rope. He makes 3 complete rounds using the rope to fence. What is the total length of rope used?

(a) 44 m

(b) 66 m

(c) 132 m

(d) 363 m

**Question.6.** The perimeter of a square is 2k cm. If the perimeter of square becomes \frac{1}{2}k cm, how will the side length of the square change?

(a) It will become 4 times

(b) It will become 8 times

(c) It will become one-fourth

(d) It will become one-eighth

**Ans.5.** (c) 132 m**Ans.6.** (c) It will become one-fourth

**Hint:** Deduce and generalize the formula to determine the perimeter of a regular polygon.

**Question.7.** A wire of length 56 cm is made into the shape of a heptagon. What is the side length of the heptagon?

(a) 7 cm

(b) 8 cm

(c) 14 cm

(d) 49 cm

**Question.8.** The perimeter of a regular hexagon is 14 cm less than the perimeter of a regular octagon. If the side length of the hexagon is (2k+3) cm, what is the side length of the octagon?

(a) (2k+5) cm

(b) (2k-13) cm

(c) \frac{1}{2}(3k+1) cm

(d) \left(\frac{3}{2}k+4\right) cm

**Ans.7.** (b) 8 cm**Ans.8.** (d) \left(\frac{3}{2}k+4\right) cm

**Hint:** Give examples in order to defend that different shapes can have the same perimeter.

**Question.9.** Consider two shapes shown.Given that the perimeter of the two shapes is equal, what is the value of x?

(a) 5

(b) 8

(c) 10

(d) 16

**Question.10.** Consider a figure below.Which of these has the same perimeter as figure A?

(a) A rectangle of length 12 cm and breadth 6 cm.

(b) An equilateral triangle of side length 24 cm.

(c) A regular pentagon of side length 9 cm.

(d) A square of side length 36 cm.

**Ans.9.** (a) 5**Ans.10.** (b) An equilateral triangle of side length 24 cm.

**Hint:** Count the squares in order to estimate the area of the given closed curve in the squares grid sheet.

**Question.11.** What is the area of the following figure?

(a) 13 square units

(b) 15 square units

(c) 16 square units

(d) 17 square units

**Question.12.** A farmer needs to buy seeds for a piece of agricultural land represented on a rectangular grid as shown below.He requires 4 bags of seeds for each square unit. What is the total number of bags required for the land?

(a) 18.5

(b) 22.5

(c) 74

(d) 78

**Ans.11.** (b) 15 square units**Ans.12.** (c) 74

**Hint:** Deduce and apply the formula in order to determine the area of a rectangle.

**Question.13.** The length of a rectangle is twice its breadth. Given that the length of the rectangle is 8 cm, what is the area of the rectangle?

(a) 24 cm^{2}

(b) 32 cm^{2}

(c) 48 cm^{2}

(d) 128 cm^{2}

**Question.14.** The length and breadth of a rectangle are changed such that the area of the rectangle changes from 2k to k. If the length and breadth of the original rectangle are l and b respectively, which of these could be the length and breadth of the new rectangle?

(a) \frac{l}{4} and 2b

(b) \frac{l}{2} and \frac{b}{2}

(c) \frac{l}{2} and 4b

(d) \frac{l}{4} and 4b

**Ans.13.** (b) 32 cm^{2}**Ans.14.** (a) \frac{l}{4} and 2b

**Hint:** Deduce and apply the formula in order to determine the area of a square.

**Question.15.** Observe the figure below:What is the area of the shaded region?

(a) 14 cm^{2}

(b) 28 cm^{2}

(c) 301 cm^{2}

(d) 949 cm^{2}

**Question.16.** If the side length of a square becomes one-third of the original side length, what is the ratio of the area of the original square to the area of square with changed side length?

(a) 1:3

(b) 1:9

(c) 3:1

(d) 9:1

**Ans.15.** (c) 301 cm^{2}**Ans.16.** (d) 9:1