A triangle has corners at (0, 0), (8, 0) and (3, 6) on a grid. Find its area.

1/2 × 8 × 6 = 24 square units

Free worksheet · Australian Curriculum

Area of a triangle worksheets with answers

The area of a triangle is half the base times the perpendicular height. Learn when and how to use it, then make a free worksheet with full solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Area of a triangle, explained

One formula, and one thing to watch: the height must be perpendicular to the base.

1. The formula

$A = \frac{1}{2} \times b \times h$ A triangle is half of a rectangle with the same base and height, which is where the half comes from. For $b = 8$ cm and $h = 5$ cm:

$A = \frac{1}{2} \times 8 \times 5 = 20 \text{ cm}^2$

2. Use the perpendicular height

The height is the distance from the base to the opposite corner, measured at right angles to the base. It is often shown as a dashed line with a small square. A sloping side is not the height, and using it is the most common mistake.

3. Right-angled triangles

In a right-angled triangle, the two sides that meet at the right angle are the base and the height. With those sides $6$ cm and $9$ cm:

$A = \frac{1}{2} \times 6 \times 9 = 27 \text{ cm}^2$

4. Obtuse triangles

In an obtuse triangle the height can fall outside the triangle, along an extended base. The formula is the same: a base of $7$ cm and a height of $4$ cm still gives

$A = \frac{1}{2} \times 7 \times 4 = 14 \text{ cm}^2$

5. Finding a missing base or height

Substitute what you know and solve. If the area is $36$ cm² and the base is $9$ cm:

$36 = \frac{1}{2} \times 9 \times h, 36 = 4.5h, h = 8 \text{ cm}$

6. Word problems

A triangular sail has a base of $3$ m and a height of $4.5$ m:

$A = \frac{1}{2} \times 3 \times 4.5 = 6.75 \text{ m}^2$

Check the units are the same before you multiply, and give the answer in square units.

Quick check: 10 questions

Try each one, then open the answer.

Find the area of a triangle with base $10$ cm and height $6$ cm.
Answer
$30$ cm²
Find the area of a triangle with base $7$ m and height $4$ m.
Answer
$14$ m²
A right-angled triangle has shorter sides $5$ cm and $12$ cm. Find its area.
Answer
$30$ cm²
Find the area of a triangle with base $9$ cm and height $5$ cm.
Answer
$22.5$ cm²
Find the area of a triangle with base $2.4$ m and height $1.5$ m.
Answer
$1.8$ m²
A triangle has an area of $40$ cm² and a base of $10$ cm. Find its height.
Answer
$8$ cm
A triangle has an area of $27$ m² and a height of $6$ m. Find its base.
Answer
$9$ m
A triangle has sides $3$ cm, $4$ cm and $5$ cm, with a right angle between the $3$ cm and $4$ cm sides. Find its area.
Answer
$6$ cm²
A triangle has corners at $(0, 0)$ , $(8, 0)$ and $(3, 6)$ on a grid. Find its area.
Answer
$\frac{1}{2} \times 8 \times 6 = 24$ square units
A triangular garden bed has a base of $6$ m and a height of $4$ m. Soil costs $12 per square metre. How much will the soil cost?
Answer
Area $= 12$ m², so $144

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetArea and perimeter Year 8 worksheetArea and perimeter Year 7 worksheetAngles in triangles and quadrilaterals Year 8 worksheetPythagoras' theorem

Questions

What is the formula for the area of a triangle?

Area equals half the base times the perpendicular height. The height must be measured at right angles to the base, not along a sloping side.

Does the formula work for every triangle?

Yes. It works for right-angled, acute and obtuse triangles. For an obtuse triangle the height may fall outside the triangle, but the formula is the same.

Do the worksheets include answers?

Yes. Every question on a generated worksheet comes with a fully worked solution, so students can check each step.

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