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Year 6 Maths

Area Formulas

Learn the formulas for calculating the area of triangles, parallelograms, and composite shapes.

Quick Review: Area of a Rectangle

You already know that for a rectangle, the area is length × width. We build on this for other shapes.

Area = length × width

8 cm 5 cm

Area = 8 × 5 = 40 cm²

Area of a Triangle

A triangle is exactly half of a rectangle. If you draw a rectangle around any triangle, the triangle fills exactly half.

Area = ½ × base × height

1

Find the area: base = 10 cm, height = 6 cm

Step 1: Write the formula: A = ½ × b × h

Step 2: Substitute: A = ½ × 10 × 6 = ½ × 60

Step 3: A = 30 cm²

Area of a Parallelogram

A parallelogram can be rearranged into a rectangle by cutting off a triangle from one side and moving it to the other.

Area = base × height

The height is the perpendicular distance, not the slant side!

2

Find the area: base = 9 cm, height = 4 cm

Step 1: A = base × height

Step 2: A = 9 × 4 = 36 cm²

Composite Shapes

A composite shape is made up of two or more simple shapes joined together. Break the shape into parts, find each area, then add them up.

3

An L-shape made of two rectangles: 6×4 and 3×2

Step 1: Area of rectangle 1 = 6 × 4 = 24 cm²

Step 2: Area of rectangle 2 = 3 × 2 = 6 cm²

Step 3: Total area = 24 + 6 = 30 cm²

Knowledge Check

Select the correct answer for each question. Questions get harder as you go!

Question 1

What is the area of a triangle with base = 8 cm and height = 4 cm?

Question 2

What is the area of a parallelogram with base = 7 cm and height = 5 cm?

Question 3

The formula for the area of a triangle is:

Question 4

A triangle has an area of 24 cm² and a base of 8 cm. What is its height?

Question 5

A parallelogram has a base of 12 cm and a slant side of 7 cm. The perpendicular height is 5 cm. What is the area?

Question 6

A composite shape is made of a rectangle (10 × 4 cm) with a triangle on top (base 10 cm, height 3 cm). What is the total area?

Question 7

A triangle and a parallelogram have the same base (10 cm) and the same height (6 cm). The triangle’s area is what fraction of the parallelogram’s area?

Question 8

An L-shaped room is made of two rectangles: one is 5 m × 8 m and the other is 3 m × 4 m. What is the total floor area?

Question 9

A parallelogram has an area of 72 cm² and a height of 8 cm. What is its base?

Question 10

A garden is shaped like a rectangle (12 m × 8 m) with a triangular section removed (base 4 m, height 3 m). What is the remaining area?

Key Concepts Summary