Area of Rectangles and Triangles

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 →

Area of a Rectangle

Area measures the space inside a 2D shape. For a rectangle, you can count the unit squares inside — or simply multiply the two dimensions.

A = l × w (also written A = b × h)

Example 1: Rectangle 8 cm × 5 cm — count the grid 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)

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

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

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.

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?

Area of Rectangles and Triangles

Learning Objectives

Real-World Applications

Subscribe to keep learning

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

Practice: Extra Questions

⚠ Things to Watch Out For