Perimeter and area Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Perimeter and area questions. See exactly how to solve problems on area of a rectangle, length times width, decimal lengths, perimeter.

area of a rectanglelength times widthdecimal lengthsperimeterdistance round a shapearea of a triangle
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
The diagram shows a rectangle measuring 88 cm by 55 cm. Work out the area of the rectangle.

Worked solution

  1. Write down the rule for the area of a rectangle.

    A=l×wA = l \times w

    The area of a rectangle is its length multiplied by its width.

  2. Substitute the length and the width into the rule.

    A=8×5A = 8 \times 5

    The rectangle is 88 cm long and 55 cm wide.

  3. Work out the area of the rectangle.

    A=40 cm2A = 40\text{ cm}^2

    The area is 4040 square centimetres.

Answer
A=40 cm2A = 40\text{ cm}^2
Question 2
1 markeasy
The diagram shows a rectangle measuring 1212 cm by 77 cm. Work out the area of the rectangle.

Worked solution

  1. Write down the rule for the area of a rectangle.

    A=l×wA = l \times w

    The area of a rectangle is its length multiplied by its width.

  2. Substitute the length and the width into the rule.

    A=12×7A = 12 \times 7

    The rectangle is 1212 cm long and 77 cm wide.

  3. Work out the area of the rectangle.

    A=84 cm2A = 84\text{ cm}^2

    The area is 8484 square centimetres.

Answer
A=84 cm2A = 84\text{ cm}^2
Question 3
2 markseasy
The diagram shows a rectangle measuring 7.57.5 cm by 44 cm. Work out the area of the rectangle.

Worked solution

  1. Write down the rule for the area of a rectangle.

    A=l×wA = l \times w

    The area of a rectangle is its length multiplied by its width.

  2. Substitute the length and the width into the rule.

    A=7.5×4A = 7.5 \times 4

    The rectangle is 7.57.5 cm long and 44 cm wide.

  3. Work out the area of the rectangle.

    A=30 cm2A = 30\text{ cm}^2

    The area is 3030 square centimetres.

Answer
A=30 cm2A = 30\text{ cm}^2
Question 4
2 markseasy
The diagram shows a rectangle measuring 88 cm by 55 cm. Work out the perimeter of the rectangle.

Worked solution

  1. Write down the rule for the perimeter of a rectangle.

    P=2(l+w)P = 2(l + w)

    The perimeter is the total distance round the outside. A rectangle has two lengths and two widths, so P=2(l+w)P = 2(l + w).

  2. Add the length and the width, then double the result.

    P=2×(8+5)=2×13P = 2 \times (8 + 5) = 2 \times 13

    One length and one width together are 1313 cm; the rectangle has two of each.

  3. Work out the perimeter of the rectangle.

    P=26 cmP = 26\text{ cm}

    The perimeter is 2626 cm.

Answer
P=26 cmP = 26\text{ cm}
Question 5
1 markeasy
The diagram shows a rectangle measuring 1111 cm by 66 cm. Work out the perimeter of the rectangle.

Worked solution

  1. Write down the rule for the perimeter of a rectangle.

    P=2(l+w)P = 2(l + w)

    The perimeter is the total distance round the outside. A rectangle has two lengths and two widths, so P=2(l+w)P = 2(l + w).

  2. Add the length and the width, then double the result.

    P=2×(11+6)=2×17P = 2 \times (11 + 6) = 2 \times 17

    One length and one width together are 1717 cm; the rectangle has two of each.

  3. Work out the perimeter of the rectangle.

    P=34 cmP = 34\text{ cm}

    The perimeter is 3434 cm.

Answer
P=34 cmP = 34\text{ cm}

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