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Area and Perimeter Word Problems Quiz - CBSE Class 7 Mathematics

Free practice quiz: Area and Perimeter Word Problems (CBSE Class 7 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 19 multiple-choice questions on Area and Perimeter Word Problems, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Perimeter of rectangles and squares

  • Perimeter is the total length of the boundary around a shape.
  • Fencing, border, frame or wire around a shape all mean perimeter. It is measured in cm or m.
  • For going around more than once, multiply the perimeter by the number of rounds.
Perimeter of rectangle
\[P = 2(l + b)\]
Perimeter of square
\[P = 4a\]
Wire for n rounds
\[\text{Total length} = n \times P\]

Common mistake: Adding length and breadth only once, giving l + b instead of 2(l + b).

Area of rectangles and squares

  • Area is the amount of surface a flat shape covers.
  • Area is measured in square units, like cm² or m².
  • Covering, carpeting, painting or tiling a surface usually means area.
Area of rectangle
\[A = l \times b\]
Area of square
\[A = a^2\]

Common mistake: Writing area in cm or m instead of square units like cm² or m², or mixing up area and perimeter.

Finding a missing side

  • If area or perimeter and one side are known, work backwards to find the other side.
  • If one side is a multiple of the other, write both sides using one letter, like kb and b.
Breadth from area
\[b = \frac{A}{l}\]
Breadth from perimeter
\[b = \frac{P}{2} - l\]
Length is k times breadth
\[P = 2(kb + b) = 2b(k + 1)\]

Common mistake: Dividing the perimeter by 2 and stopping, forgetting to subtract the known length afterwards.

Area of triangle and trapezium

  • A triangle covers half the area of a rectangle with the same base and height.
  • A trapezium has two parallel sides. Add them, halve the sum, then multiply by the height.
Area of triangle
\[A = \frac{1}{2} \times b \times h\]
Area of trapezium
\[A = \frac{1}{2}(a + b) \times h\]

Common mistake: Forgetting the one-half, or using a slanting side instead of the perpendicular height.

Effect of changing the sides

  • If every side is multiplied by k, the perimeter is also multiplied by k.
  • The area is multiplied by k², because both length and breadth change.
New perimeter
\[P_{\text{new}} = k \times P\]
New area
\[A_{\text{new}} = k^2 \times A\]

Common mistake: Thinking the area is multiplied by k, just like the perimeter, instead of by k².

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. A rectangle has a length of 10 cm and a width of 5 cm. What is its perimeter?

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    Answer: A. 30 cm

    The perimeter of a rectangle is calculated as 2 times the sum of its length and width. Therefore, perimeter = 2 * (10 + 5) = 30 cm.

  2. The perimeter of a rectangular field is 60 meters. If the length is 18 meters, what is the width?

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    Answer: A. 12 meters

    The perimeter P of a rectangle is given by P = 2 * (length + width). With a perimeter of 60 and length of 18, solve for width: 60 = 2 * (18 + width). Hence, width = 12 meters.

  3. What is the area of a rectangle with dimensions 16 cm x 5 cm?

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    Answer: A. 80 square cm

    The area of a rectangle is given by length multiplied by width. Area = 16 * 5 = 80 square cm.

  4. Find the border length needed for a square garden with a side of 15 meters.

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    Answer: A. 60 meters

    The perimeter of a square is calculated as 4 times one side. Therefore, perimeter = 4 * 15 = 60 meters.

  5. A triangle has a base of 14 cm and a height of 10 cm. What is its area?

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    Answer: A. 70 square cm

    Area of a triangle is (base * height) / 2. Substituting values, Area = (14 * 10) / 2 = 70 square cm.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. A square has a side length of 8 cm. What is its perimeter?
  2. A rectangle has an area of 45 square meters and a length of 9 meters. What is its width?
  3. Find the area of a square garden with a side length of 7 meters.
  4. Calculate the area of a rectangle with a length of 12 cm and width of 3 cm.
  5. A farmer wants to fence his square plot of land, which has a side of 20 m. How much fencing material will he need?
  6. A playground is in the shape of a rectangle with a length of 40 meters and width of 30 meters. What is the perimeter of the playground?
  7. Calculate the fencing needed for a rectangular field where length is 25 meters and width is 10 meters.
  8. A rectangular swimming pool is 50 meters long and 20 meters wide. Compute its area.
  9. A table top is in the form of a rectangle. It has a length of 120 cm and a width of 90 cm. What is the area?
  10. If the side of a square is doubled, how does the perimeter change?
  11. The area of a rectangular park is 540 square meters. If the length is 30 meters, find the width.
  12. The length of a rectangle is twice its width. If the perimeter is 60 cm, what are the dimensions?
  13. What is the area of a trapezium with bases 10 cm and 20 cm, and a height of 5 cm?
  14. A rectangular plot is 15 meters long and 10 meters wide. How much wire is needed to go around it twice?

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