Area of a Triangle Calculator

Last updated: 27 Nov 2025 | Author: Brij | Review By: Irshad

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Calculate the area of a triangle instantly using base and height. This simple Area of Triangle Calculator uses the formula ½ × base × height. Includes formula, and worked example.

Calculation Method:

Base & Height Three Sides (SSS) Two Sides + Angle (SAS) Two Angles + Side (ASA)

Base (b):

units

Height (h):

units

Side a:

units

Side b:

units

Side c:

units

Side a:

units

Side b:

units

Angle C (between):

Angle A:

Angle B:

Side c (between):

units

Triangle Calculation Results

Area of Triangle:

sq unit

Perimeter:

Angle A:

Angle B:

Angle C:

Finding the area of a triangle is one of the most common geometry tasks. The simplest and most widely used method is based on the base and height of the triangle. This calculator uses exactly that approach: you enter the base length and height, and it instantly returns the triangle’s area.

1. Triangle Area Formula (Base and Height)

The area of any triangle using base and height is:

$Area = \frac{1}{2} \times b \times h$

Where:

b = base length
h = perpendicular height

This formula works for all triangle types — scalene, isosceles, or equilateral — as long as you know a base side and the perpendicular height drawn to that base.

Worked Example

Let’s calculate the area using:

Base b=10b = 10
b=10 units
Height h=6h = 6
h=6 units

Step 1 — Apply the Formula

$Area = \frac{1}{2} \times 10 \times 6$

Step 2 — Multiply

$Area = \frac{1}{2} \times 60 = 30$

Final Answer

$Area = 30\ \text{square units}$

2. Area of Triangle Using Three Sides (SSS Method)

This method is used when you know all three sides of a triangle:

Side a
Side b
Side c

We use Heron’s Formula.

Heron’s Formula for Area

Step 1 — Compute the Semi-Perimeter

$s = \frac{a + b + c}{2}$

Step 2 — Calculate Area

$Area = \sqrt{s(s - a)(s - b)(s - c)}$

Worked Example (SSS Method)

Let’s say the triangle has:

a = 7
b = 8
c = 5

Step 1 — Find the Semi-Perimeter

$s = \frac{7 + 8 + 5}{2} = 10$

Step 2 — Apply Heron’s Formula

$Area = \sqrt{10(10 - 7)(10 - 8)(10 - 5)}$

Step 3 — Final Answer

$Area = \sqrt{300} \approx 17.32$

3. Area of Triangle Using Two Sides and the Included Angle (SAS Method)

When you know two sides of a triangle and the angle between them, you can calculate the area using the SAS formula.

This method is extremely useful when:

No height is given
No perpendicular measurement is available
Only two side lengths and the included angle are known

Example situations include surveying, navigation, and trigonometric constructions.

Formula

If you know:

Side a
Side b
Included angle C

Then the area is:

$Area = \frac{1}{2}ab\sin(C)$

Worked Example

Suppose we know:

a = 9
b = 12
C = $40^\circ$

Step 1 — Apply the Formula

$Area = \frac{1}{2} \times 9 \times 12 \times \sin(40^\circ)$

Step 2 — Multiply Numbers

$Area = 54 \times \sin(40^\circ)$

Step 3 — Final Answer

$Area = 54 \times 0.6428 = 34.71$

Area of Triangle Using Two Angles and the Included Side (ASA Method)

When you know two angles of a triangle and the side between them, you can calculate the area using trigonometry.

This situation happens in navigation, surveying, geometry problems, and construction layout.

ASA works because if you know:

Angle A
Angle B
Side c between them

…then the entire triangle can be solved using the Law of Sines.

Once the remaining sides are known, the standard triangle area formula can be applied.

ASA Area Formula

Step 1 — Find the third angle

$C = 180^\circ - (A + B)$

Step 2 — Use Law of Sines to find the other sides

$a = \frac{c \sin(A)}{\sin(C)}$

$b = \frac{c \sin(B)}{\sin(C)}$

Step 3 — Use the SAS Area Formula

Now that you know sides a and b, and angle C between them:

$Area = \frac{1}{2}ab\sin(C)$

Worked Example (ASA)

Given:

Angle $A = 50^\circ$
Angle $B = 60^\circ$
Side $c = 12$ (between angles A and B)

Step 1 — Find Angle C

$C = 180^\circ - (50^\circ + 60^\circ) = 70^\circ$

Step 2 — Use Law of Sines

Find side a:

$a = \frac{12 \sin(50^\circ)}{\sin(70^\circ)} = 9.79$

Find side b:

$b = \frac{12 \sin(60^\circ)}{\sin(70^\circ)} = 11.06$

Step 3 — Area Using SAS

$Area = \frac{1}{2}(9.79)(11.06)\sin(70^\circ) = 50.92$

FAQs About Area of a Triangle

1. Which formula should I use to find the area of a triangle?

It depends on what information you have:

Base + Height → use $\frac{1}{2}bh$
Three sides (SSS) → use Heron’s Formula
Two sides + included angle (SAS) → use $\frac{1}{2}ab\sin(C)$
Two angles + included side (ASA) → find the other sides using Law of Sines, then apply SAS

Your calculator automatically chooses the correct method based on the inputs you provide.

2. What is the easiest way to calculate the area?

The easiest formula is:

$Area = \frac{1}{2}bh$

But this only works if you know the height (perpendicular to the base).

If height is unknown, SAS or SSS are usually more practical.

3. When should I use Heron’s Formula?

Use Heron’s Formula when you only know the three sides of a triangle (SSS), and no angle or height is given.

It works for all triangle shapes, even very irregular ones.

4. Can the area be calculated using only angles?

No — you cannot find the area using only angles.

You must know at least one side length (plus another angle or side) to convert that angle information into actual dimensions.

5. What if my triangle sides don’t satisfy the triangle inequality?

For any valid triangle:

$a + b > c,\quad b + c > a,\quad a + c > b$

If your inputs violate this rule, the triangle does not exist, and the calculator should display an error.

This happens often with SSS input mistakes.

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