Home / Level 2 Course
Functional Skills Level 2 — Shape: Perimeter and Area

Area of Rectangles and Triangles

← Previous Back to Course Next Lesson →

Learning Objectives

Real-World Applications

Subscribe to keep learning

You’ve seen the first part of this lesson for free. Log in and subscribe to unlock the rest, plus every other lesson, worksheet and checkpoint paper.

See Plans →

How Do You Find the Area of a Rectangle?

Area measures the amount of space inside a 2D shape, in square units. For a rectangle, multiply its length by its width: Area = length × width. You can check this by counting the unit squares that fit inside the rectangle.

A = l × w   (also written A = b × h)
Example 1: Rectangle 8 cm × 5 cm — count the grid squares
8 cm 5 cm Area = 8 × 5 = 40 cm² Each small square = 1 cm² - count 40 squares
Step 1
Write the formula: \(A = l \times w\)
Step 2
Substitute: \(A = 8 \times 5 = \mathbf{40 \text{ cm}^2}\)
Tip: The grid shows why the formula works — you are literally counting rows of squares. 5 rows of 8 squares each = 40 squares.
Example 2: A room is 6.5 m by 4.2 m. Find its area.
Step 1
\(A = 6.5 \times 4.2 = \mathbf{27.3 \text{ m}^2}\)

✓ Quick Check 1 — Area of Rectangles

Question 1 of 10

Area of a Triangle

A triangle is always half of a rectangle with the same base and height. That is why we divide by 2.

A = ½ × b × h
Key definition: h is the perpendicular height — the distance measured at 90° to the base. It is NOT the slant side of the triangle.
Why ½? — Triangle as half a rectangle (base 12 cm, height 8 cm)
other half of rectangle base = 12 cm h = 8 cm Triangle = half the rectangle Area = ½ × 12 × 8 = 48 cm²
Step 1
\(A = \dfrac{1}{2} \times 12 \times 8\)
Step 2
\(A = \dfrac{1}{2} \times 96 = \mathbf{48 \text{ cm}^2}\)
Example 3: Right-angled triangle — base 9 cm, height 6 cm
base = 9 cm height = 6 cm A = ½ × 9 × 6 = 27 cm² For right triangles: the two legs are the base and height
Step 1
The two legs of the right angle act as base and height: \(b = 9\text{ cm},\ h = 6\text{ cm}\)
Step 2
\(A = \dfrac{1}{2} \times 9 \times 6 = \mathbf{27 \text{ cm}^2}\)
Example 4: Non-right triangle — perpendicular height
h base (b) NOT this (slant side) h must be perpendicular (90°) to the base — NOT the slant side
Warning: Always use the perpendicular height (shown by the dashed blue line). The slant side of the triangle is longer — using it will give a wrong answer.

✓ Quick Check 2 — Area of Triangles

Question 1 of 10

Compound Shapes — Rectangles and Triangles Together

A compound shape is made of two or more simple shapes joined together. Split it into a rectangle and a triangle (or more than one of each), find each area separately, then add them together.

8 m × 4 m base 8 m, height 3 m Split into: rectangle (body) + triangle (roof)

Example 5 — Find the total area of the house-shaped figure above

Step 1 — Rectangle (body)
\(A = 8 \times 4 = 32\text{ m}^2\)
Step 2 — Triangle (roof)
\(A = \frac{1}{2} \times 8 \times 3 = 12\text{ m}^2\)
Step 3 — Add the parts
\(32 + 12 = \mathbf{44\text{ m}^2}\)
⚠ Common mistake: Don't double-count a shared edge or accidentally include it as extra area — the line where the rectangle and triangle meet (the "8 m" base of the roof) is a boundary you split *along*, not a separate piece of area.

✓ Quick Check 3 — Mixed: Missing Dimensions and Word Problems

Question 1 of 10

Practice: Extra Questions

Work out each answer, then type it in and click Check to see if you're right.

# Question Your answer Result
1 Rectangle: length = 8 cm, width = 5 cm. Area = ?
2 Rectangle: length = 12 cm, width = 4 cm. Area = ?
3 Triangle: base = 10 cm, height = 6 cm. Area = ½ × 10 × 6 = ?
4 Triangle: base = 8 cm, height = 7 cm. Area = ?
5 Rectangle: length = 9 cm, width = 3 cm. Area = ?
6 Triangle: base = 14 cm, height = 5 cm. Area = ?
7 Rectangle: length = 6 cm, width = 6 cm. Area = ?
8 Rectangle: 7 cm × 4 cm. Area = ?
9 Rectangle: 12 m × 3.5 m. Area = ?
10 Right triangle: base = 10 cm, height = 6 cm. Area = ?
11 Triangle: base = 8 m, height = 5 m. Area = ?
12 Rectangle: 15 mm × 9 mm. Area = ?
13 Triangle: base = 14 cm, height = 9 cm. Area = ?

⚠ Things to Watch Out For

  • For triangles, always use the perpendicular height — not the slant side — in the formula ½ × base × height.
  • Don't confuse area (the space inside) with perimeter (the distance around the outside).
  • Area is always measured in square units (cm², m², etc.) — include the correct unit in your answer.
  • A square is a special rectangle — you can use length × width, which gives length².
  • For compound shapes made of rectangles and triangles, split the shape and add (or subtract) the parts carefully.
What would you like to do next?
← Previous Next Lesson → Return to Course 📄 Go to the Worksheet 🎯 Try the Topic Drill