The most crucial thing is that the base and also height are at appropriate angles. Have actually a play here:

### Example: What is the area of this triangle?

(Note: 12 is the height, no the length of the left-hand side)

Height = h = 12

Base = b = 20

Area = ½ bh = ½ × 20 × 12 = 120

## Knowing 3 Sides

There"s additionally a formula to discover the area of any kind of triangle when we understand the lengths the all 3 of that is sides.

You are watching: How do you find the area of a scalene triangle

This can be uncovered on the Heron"s Formula page.

## Knowing two Sides and the had Angle

When we know two sides and the included angle (SAS), there is an additional formula (in reality three indistinguishable formulas) we can use.

Depending on which sides and also angles us know, the formula can be created in three ways:

Area = 12ab sin C

Area = 12bc sin A

Area = 12ca sin B

They space really the very same formula, simply with the sides and also angle changed.

### Example: find the area of this triangle:

First of every we need to decide what we know.

We recognize angle C = 25º, and sides a = 7 and also b = 10.

So let"s obtain going:

## How to Remember

Just think "abc": Area = ½ a b sin C

It is also great to remember the the edge is constantly between the two recognized sides, referred to as the "included angle".

## How Does it Work?

We begin with this formula:

Area = ½ × basic × height

We understand the base is c, and can work-related out the height:

the elevation is b × sin A

So we get:

Area = ½ × (c) × (b × sin A)

Which deserve to be simplified to:

Area = 12bc sin A

By an altering the labels on the triangle us can likewise get:

Area = ½ ab sin C Area = ½ ca sin B

One an ext example:

### Example: discover How lot Land

Farmer Rigby own a triangular item of land.

The size of the fence ab is 150 m. The size of the fence BC is 231 m.

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The angle in between fence ab and fence BC is 123º.

How much land does Farmer Rigby own?

First of all we need to decide which lengths and angles we know:

abdominal = c = 150 m, BC = a = 231 m, and also angle B = 123º

So us use:

Area = 12ca sin B

Put in the worths we know:½ × 150 × 231 × sin(123º) m2
Do some calculator work:17,325 × 0.838... M2
Area =14,530 m2

Farmer Rigby has 14,530 m2 the land

259, 1520, 1521, 1522,260, 1523, 2344, 2345, 3940, 3941
Heron"s Formula The legislation of Sines The law of Cosines addressing Triangles Trigonometry index Algebra Index