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Perimeter and Area Quiz - CBSE Class 6 Mathematics

Free practice quiz: Perimeter and Area (CBSE Class 6 Mathematics). 14 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 14 multiple-choice questions on Perimeter and Area, and 14 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: Distance Around a Shape

  • Perimeter is the total length of the boundary of a closed shape.
  • Add the lengths of all sides. Fencing or border questions are asking for perimeter.
Rectangle (length l, breadth b)
\[P = 2(l + b)\]
Square (side a)
\[P = 4a\]
Regular polygon with n equal sides of length a
\[P = n \times a\]
Triangle with sides a, b, c
\[P = a + b + c\]

Common mistake: Adding only length and breadth once for a rectangle, forgetting there are two lengths and two breadths.

Area of Rectangles and Squares

  • Area is the amount of surface a flat shape covers, measured in square units.
  • If you know the area and one side, divide to find the other side.
Area of rectangle
\[A = l \times b\]
Area of square
\[A = a^2\]
Missing breadth
\[b = \frac{A}{l}\]

Common mistake: Writing area in cm or m instead of square units like cm² or m².

Area of Triangles and Circles

  • A triangle's area is half of a rectangle with the same base and height.
  • A circle's area depends on its radius r. Use the value of π given in the question.
Area of triangle (base b, height h)
\[A = \frac{1}{2} \times b \times h\]
Area of circle (radius r)
\[A = \pi r^2\]

Common mistake: Forgetting the half in the triangle formula, or using the diameter instead of the radius for a circle.

Finding Unknown Sides and Changes

  • Use a letter like x for an unknown side, then write other sides using x.
  • When sides change, find the new side lengths first, then calculate the new area.
Third side of a triangle from perimeter
\[c = P - a - b\]
Rectangle with length k times breadth x
\[P = 2(kx + x)\]
Length decreased by p percent
\[l_{\text{new}} = l \times \left(1 - \frac{p}{100}\right)\]
Square side increased by d
\[A_{\text{new}} = (a + d)^2\]

Common mistake: Increasing the area by the same amount as the side. Always change the side first, then square it.

Exam tips

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

Sample questions

  1. What is the perimeter of a rectangle with length 5 cm and width 3 cm?

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    Answer: B. 16 cm

    The perimeter of a rectangle is calculated by the formula P = 2(length + width). So, P = 2(5 + 3) = 16 cm.

  2. What is the perimeter of a pentagon with each side measuring 5 cm?

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    Answer: A. 25 cm

    The perimeter of a polygon is the sum of the lengths of all its sides. For a pentagon with each side measuring 5 cm: 5 × 5 = 25 cm.

  3. Find the area of a triangle with a base of 10 cm and a height of 5 cm.

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    Answer: A. 25 cm²

    The area of a triangle is calculated using the formula A = 1/2 × base × height. Thus, A = 1/2 × 10 × 5 = 25 cm².

  4. If a rectangular plot has a width of 15 m and a length of 25 m, find the perimeter of the plot.

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    Answer: B. 80 m

    Perimeter = 2(length + width) = 2(25 + 15) = 80 m.

  5. How much fencing is required to enclose a rectangular playground whose dimensions are 12 m by 14 m?

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    Answer: A. 52 m

    Fencing required is the perimeter, calculated as 2(length + width) = 2(12 + 14) = 52 m.

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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 4 cm. What is its perimeter?
  2. A park is in the shape of a rectangle with a length of 50 m and width of 30 m. What is the area of the park?
  3. If each side of a square is increased by 2 cm, and the original side length was 6 cm, what is the area of the new square?
  4. A circular garden has a radius of 7 m. What is the area of the garden? (Use π = 22/7)
  5. A farmer wants to enclose a rectangular field of area 1800 m². If the length is 45 m, what is the width?
  6. The length of a rectangle is 3 times its width. If the perimeter is 48 m, find the dimensions of the rectangle.
  7. Find the area of a rectangle if its length is decreased by 10% and the width remains the same. Length was originally 50 cm and width is 20 cm.
  8. A field is in the shape of a rectangle with a length that is 5 m longer than twice its width. If the width is 10 m, what is the perimeter of the field?
  9. If a triangle has a perimeter of 60 cm and two sides measure 20 cm and 15 cm, what is the length of the third side?

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