## MCQ on Perimeter and Area Class 6

### Class 6 Maths Chapter 6 MCQ Perimeter and Area

Question 1.

Following figures are formed by joining six unit squares. Which figure has smallest perimeter? (NCERT Exemplar)

(a) (ii)

(b) (iii)

(c) (iv)

(d) (i)

Answer:

(d) (i)

Question 2.

A square shaped park ABCD of side 100 m has two equal rectangular flower beds each of size 10m* 5 m (see figure). Length of the boundary of the remaining park is (NCERT Exemplar)

(a) 360 m

(b) 400 m

(c) 340 m

(d) 460 m

Answer:

(b) 400 m

Question 3.

Perimeter of a square =

(a) 4 × Length of a side

(b) 2 × Length of a side

(c) 3 × Length of a side

(d) 6 × Length of a side.

Answer:

(a) 4 × Length of a side

Question 4.

Perimeter of an equilateral triangle =

(a) 2 × Length of a side

(b) 3 × Length of a side

(c) 4 × Length of a side

(d) 6 × Length of a side.

Answer:

(b) 3 × Length of a side

Question 5.

Area of a rectangle =

(a) Length × Breadth

(b) Length + Breadth

(c) 2 × (Length + Breadth)

(d) 2 × (Length × Breadth).

Answer:

(a) Length × Breadth

Question 6.

The perimeter of the figure A 2m B

(a) 8 m

(b) 16 m

(c) 4 m

(d) none of these.

Answer:

(a) 8 m

Question 7.

The perimeter of the figure

(a) 20 cm

(b) 10 cm

(c) 24 cm

(d) 15 cm.

Answer:

(a) 20 cm

Question 8.

An athlete takes 10 rounds of a rectangular park, 40 m long and 30 m wide. Find the total distance covered by him.

(a) 1400 m

(b) 700 m

(c) 70 m

(d) 2800 m.

Answer:

(a) 1400 m

Question 9.

Find the cost of fencing a rectangular park of length 10 m and breadth 5 m at the rate of ₹ 10 per metre.

(a) ₹ 600

(b) ₹ 300

(c) ₹ 150

(d) ₹ 1200.

Answer:

(b) ₹ 300

Question 10.

Find the distance travelled by Sangeeta if she takes 5 rounds of a square park of side 10 m.

(a) 200 m

(b) 100 m

(c) 400 m

(d) 800 m.

Answer:

(a) 200 m

Question 11.

The perimeter of the figure is

(a) 15 cm

(b) 20 cm

(c) 10 cm

(d) 50 cm.

Answer:

(c) 10 cm

Question 12.

The perimeter of a triangle of sides 2 cm, 3 cm and 4 cm is

(a) 9 cm

(b) 18 cm

(c) 27 cm

(d) 36 cm.

Answer:

(a) 9 cm

Question 13.

Two sides of a triangle are 5 cm and 4 cm. The perimeter of the triangle is 12 cm. The third side has length

(a) 1 cm

(b) 2 cm

(c) 3 cm

(d) 6 cm.

Answer:

(c) 3 cm

Question 14.

The area of a rectangle of length 2 cm and breadth 1 cm is

(a) 1 cm²

(b) 2 cm²

(c) 4 cm²

(d) 8 cm²

Answer:

(b) 2 cm²

Question 15.

The area of a square of side 1 cm is

(a) 1 cm²

(b) 4 cm²

(c) 9 cm²

(d) 16 cm²

Answer:

(a) 1 cm²

Question 16.

The area of a rectangular sheet of paper is 20 cm2. Its length is 5 cm. Find its width.

(a) 1 cm

(b) 2 cm

(c) 3 cm

(d) 4 cm.

Answer:

(d) 4 cm.

Question 17.

The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?

Answer:

100 cm

Question 18.

Find the perimeter of each of the following shapes:

(a) A triangle of sides 3 cm, 4 cm and 5 cm

Answer:

12 cm

(b) An equilateral triangle of side 9 cm

Answer:

27 cm

(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.

Answer:

22 cm

Question 19.

Find the side of the square whose perimeter is 20 m.

Answer:

5 m

Question 20.

Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?

Answer:

10 m

Question 21.

Find the areas of the rectangles whose sides are:

(a) 3 cm and 4 cm

(b) 12 m and 21 m

Answer:

(a) 12 sq. m

(b) 252 sq. m

Question 22.

Find the areas of the squares whose sides are:

(a) 14 cm

(b) 5 m.

Answer:

(a) 196 sq. m

(b) 25 sq. m

Question 23.

A room is 4 m long and 3 m 50 cm wide. Flow many square metres of carpet is needed to cover the floor of the room?

Answer:

14 sq. m

Question 24.

A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?

Answer:

3 sq. m

Question 25.

What is perimeter of a rectangle =

(a) Length × Breadth

(b) Length + Breadth

(c) 2 × (Length + Breadth)

(d) 2 × (Length × Breadth).

Answer:

(a) Length × Breadth

Explanation:

(a) Perimeter of rectangle

= Length × Breadth

Question 26.

The perimeter of the figure

(a) 12 m

(b) 14 m

(c) 24 m

(d) 7 m.

Answer:

(b) 14 m

Explanation:

(b) Perimeter of the figure = 4 + 3 + 4 + 3

= 14 m

Question 27.

The perimeter of the figure 1 cm is

(a) 5 cm

(b) 10 cm

(c) 15 cm

(d) 20 cm

Answer:

(d) 20 cm

Explanation:

(d) Perimeter of the figure

= 2 + 2+1+ 2 + 2 + 1 + 2 + 2 + 1 + 2 + 2 + 1

= 20 cm

Question 28.

Two sides of a triangle are 5 cm and 4 cm. The perimeter of the triangle is 12 cm. The third side has length

(a) 1 cm

(b) 2 cm

(c) 3 cm

(d) 6 cm

Answer:

(c) 3 cm

(c) Third side of triangle

= Perimeter of triangle – Lengths of other two sides

= 12 – 5 – 4

= 3 cm

Question 29.

The perimeter of a rectangular piece of cardboard is 6 m. Its breadth is 1 m. Find its length.

(a) 1 m

(b) 2 m

(c) 3 m

(d) 6 m

Answer:

(b) 2 m

(b) Required length

= \(\frac{1}{2}\) perimeter of cardboard – breadth

= \(\frac{6}{2}\) – 1 = 2m

Question 30.

A piece of string is 30 cm long. What will be the length of each side if the string is used to form:

(a) a square ?

(b) an equilateral triangle ?

(c) a regular hexagon ?

Answer:

(a) Perimeter of a square

= 4 × Length of a side

⇒ 30 = 4 × Length of a side 30

⇒ Length of a side = \(\frac{30}{4}\) = 7.5 cm

(b) Perimeter of an equilateral triangle

= 3 × Length of a side

⇒ 30 = 3 × Length of a side

⇒ Length of a side = \(\frac{30}{3}\) = 10 cm

(c) Perimeter of a regular hexagon

= 6× Length of a side

⇒ 30 = 6 × Length of a side

⇒ Length of a side = \(\frac{30}{6}\) = 5 cm

Question 31.

Find the cost of fencing a rectangular park of length 100 m and breadth 75 m at the rate ofX 15 per metre.

Answer:

Perimeter of the rectangular park = 2 × (Length + Breadth)

= 2 × (100 m + 75 m)

= 2 × 175 m = 350 m

∴ Cost of fencing the rectangular park at the rate of ₹ 15 per metre = 350 × 15

= ₹ 5250

Question 32.

Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance ?

Answer:

Perimeter of the square park

= 4 × Length of a side

= 4 × (75 m)

= 300 m

Perimeter of the rectangular park

= 2 × (Length + Breadth)

= 2 × (60 m + 45 m)

= 2 × (105 m)

= 210 m

Since the perimeter of the rectangular park is less than the perimeter of the square park, therefore Bulbul covers less distance.

Question 33.

What is the perimeter of each of the following figured ? What do you infer from the answers ?

Answer:

Perimeter of the figure

= Sum of the lengths of all the sides

= 30 cm + 20 cm + 30 cm + 20cm

= 100 cm

Answer:

Perimeter of the figure .

= Sum of the lengths of all the sides

= 40 cm + 30 cm + 30 cm

= 100 cm

From the answers we infer that both the figures have the same perimeter.

Question 34.

Each side of a square field measures 25 m. Adjacent to this field, there is a rectangular field whose sides are in the ratio 3:2. If the perimeters of both the fields are equal, find the dimensions of the rectangular field.

Answer:

Perimeter of square field

= 4 × Length of a side

= 4 × 25 m

= 100 m

Let the length and breadth of the rectangular field be 3x m and 2x m respectively.

Then, perimeter of the rectangular field = 2 × (Length + Breadth)

= 2 × (3x m + 2x m)

= 2 × (5x m)

= 10x m

According to the question,

Perimeter of the rectangular field

= Perimeter of the square field

⇒ 10x = 100

⇒ x = \(\frac{100}{10}\) = 10

Length of the rectangular field

3x = 3 × 10 = 30m

Breadth of the rectangular field

2x = 2 × 10 = 20 m

Hence the dimensions of the rectangular field are 30 m and 20 m.

Question 35.

Find the areas of the following figures by counting squares:

Answer:

(a)

Covered Area | Number | Area Estimated (sq. units) |

Fully-filled squares | 2 | 2 × 1 = 2 |

Half-filled squares | 4 | 4 × ½ = 2 |

More than half-filled squares | — | — |

Less than half-filled squares | — | — |

∴ Total area of the figure = 2 + 2 = 4 sq. units

(b)

Covered Area | Number | Area Estimated (sq. units) |

Fully-filled squares | 4 | 4 × 1 = 4 |

Half-filled squares | 4 | 4 × ½ = 2 |

More than half-filled squares | — | — |

Less than half-filled squares | — | — |

∴ Total area of the figure = 4 + 2 = 6 sq. units

(c)

Covered Area | Number | Area Estimated (sq. units) |

Fully-filled squares | 5 | 5 × 1 = 5 |

Half-filled squares | — | — |

More than half-filled squares | — | — |

Less than half-filled squares | — | – |

∴ Total area of the figure = 5 sq. units

(d)

Covered Area | Number | Area Estimated (sq. units) |

Fully filled squares | 9 | 9 × 1 = 9 |

Half filled squares | — | — |

More than half-filled squares | — | — |

Less than half-filled squares | — | — |

∴ Total area of the figure = 9 sq. units