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8.1 Rectangles, Parallelograms and Triangles

GCSE Maths Foundation · Edexcel · Chapter 8: Perimeter, Area, and Volume 1

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: perimeter and area of rectangles, squares, parallelograms and triangles. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Find the perimeter of rectangles, triangles and shapes made from rectangles
  • Use the formulae for the area of a rectangle, a parallelogram and a triangle
  • Use the perpendicular height, not the sloping side, for area
  • Work backwards from an area or perimeter to find a missing length

Key words

  • Perimeter: The total distance around the outside of a shape. Units: cm, m, …
  • Area: The amount of flat space inside a shape. Units: cm², m², …
  • Perpendicular height: The height measured at right angles (90°) to the base.
  • Parallelogram: A four-sided shape with two pairs of parallel sides.
  • Formula: A rule written with letters, such as A = b × h.

Perimeter

Add the lengths of all the sides. For a shape made of rectangles, work out any missing sides first.

Worked example: a rectangle

A rectangle is 8 cm long and 5 cm wide.
Perimeter = 8 + 5 + 8 + 5 = 26

Answer: 26 cm

Worked example: a compound shape

Missing horizontal side = 10 − 6 = 4 cm. Missing vertical side = 7 − 4 = 3 cm.
Perimeter = 10 + 4 + 4 + 3 + 6 + 7 = 34

Answer: 34 cm

Area of rectangles and squares

Key fact: Area of a rectangle = length × width. Area of a square = side × side

Worked example: areas

A rectangle 9 cm by 6 cm: 9 × 6 = 54 cm².
A square of side 7 m: 7 × 7 = 49 m².

Answer: 54 cm² and 49 m²

Worked example: working backwards

(a) A rectangle has area 48 cm² and width 6 cm. Length = 48 ÷ 6 = 8 cm.
(b) A rectangle has perimeter 30 cm and length 9 cm. Two widths = 30 − 9 − 9 = 12, so width = 6 cm.

Answer: (a) 8 cm (b) 6 cm

Area of a parallelogram

Cut a triangle off one end of a parallelogram and move it to the other end: you get a rectangle. So the area is base × perpendicular height.

Key fact: Area of a parallelogram = base × perpendicular height (A = b × h)

Worked example: a parallelogram

Base 9 cm, perpendicular height 4 cm (the sloping side, 5 cm, is not used).
A = 9 × 4 = 36

Answer: 36 cm²

Area and perimeter of triangles

A triangle is half of a rectangle (or parallelogram) with the same base and height.

Key fact: Area of a triangle = 1/2 × base × perpendicular height (A = 1/2 × b × h)

Worked example: a right-angled triangle

The two sides at the right angle are the base and the height.
Area = 1/2 × 8 × 6 = 24 cm². Perimeter = 8 + 6 + 10 = 24 cm.

Answer: Area 24 cm², perimeter 24 cm

Worked example: an isosceles triangle

Area = 1/2 × 10 × 12 = 60 cm². Perimeter = 10 + 13 + 13 = 36 cm.

Answer: Area 60 cm², perimeter 36 cm

Worked example: finding the height

A triangle has area 30 cm² and base 12 cm.
1/2 × 12 × h = 30, so 6h = 30 and h = 5.

Answer: Height 5 cm

Common mistakes

  • Using the sloping side instead of the perpendicular height for a parallelogram or triangle.
  • Forgetting to halve when finding the area of a triangle.
  • Mixing up perimeter (cm) and area (cm²), or leaving out the units.
  • Missing out sides when finding the perimeter of a compound shape.

Revision questions

Try these, then check your answers below each one.

Question 1. A rectangle is 9 cm long and 6 cm wide. Work out its area.

Answer: 54 cm²

Working: 9 × 6 = 54 cm².

Question 2. A rectangle is 11 cm long and 4 cm wide. Work out its perimeter.

Answer: 30 cm

Working: 11 + 4 + 11 + 4 = 30 cm.

Question 3. A triangle has a base of 10 cm and a perpendicular height of 7 cm. Work out its area.

Answer: 35 cm²

Working: 1/2 × 10 × 7 = 35 cm².

Related lessons

Continue in the full course

This lesson is section 8.1 (EGCMF0801) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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