Area of Triangles

There are several ways to notice the area of a triangle.

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Knowing Base and Height

triangle b h

When we know the base and height information technology is like shooting fish in a barrel.

It is just half of b times h

Expanse = 1 2 bh

(The Triangles folio explains more)

The most of import matter is that the base and acme are at right angles. Have a play here:

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Example: What is the surface area of this triangle?

Triangle
(Note: 12 is the tiptop, not the length of the left-paw side)

Height = h = 12

Base = b = 20

Area = ½ bh = ½ × xx × 12 = 120

627,723, 3132, 3133

Knowing Three Sides

SSS Triangle

In that location's likewise a formula to notice the area of any triangle when we know the lengths of all three of its sides.

This can be found on the Heron'southward Formula page.

Knowing Two Sides and the Included Angle

SSS Triangle

When we know two sides and the included bending (SAS), there is some other formula (in fact iii equivalent formulas) we tin use.

Depending on which sides and angles we know, the formula can exist written in three ways:

Area = ane ii ab sin C

Surface area = ane ii bc sin A

Area = 1 2 ca sin B

They are actually the same formula, simply with the sides and bending changed.

Example: Find the area of this triangle:

trig area example

Beginning of all we must decide what nosotros know.

We know angle C = 25º, and sides a = 7 and b = ten.

So allow's get going:

Surface area = (½)ab sin C

Put in the values nosotros know: ½ × 7 × 10 × sin(25º)

Do some estimator piece of work: 35 × 0.4226...

Expanse = 14.eight to i decimal place

How to Remember

Only recollect "abc": Area = ½ a b sin C

Information technology is also skilful to think that the bending is always between the ii known sides, chosen the "included angle".

How Does it Piece of work?

We commencement with this formula:

Expanse = ½ × base × height

We know the base is c, and can piece of work out the height:

trig triangle b sinA
the height is b × sin A

And then nosotros get:

Area = ½ × (c) × (b × sin A)

Which can be simplified to:

Area = 1 2 bc sin A

Past changing the labels on the triangle nosotros tin can likewise become:

  • Area = ½ ab sin C
  • Area = ½ ca sin B

Ane more example:

Case: Find How Much Land

trig area example

Farmer Rigby owns a triangular piece of country.

The length of the argue AB is 150 chiliad. The length of the debate BC is 231 grand.

The angle between fence AB and fence BC is 123º.

How much land does Farmer Rigby ain?

First of all nosotros must make up one's mind which lengths and angles nosotros know:

  • AB = c = 150 m,
  • BC = a = 231 k,
  • and bending B = 123º

So we apply:

Surface area = 1 2 ca sin B

Put in the values we know: ½ × 150 × 231 × sin(123º) g2

Do some calculator work: 17,325 × 0.838... g2

 Area = xiv,530 thousandii

Farmer Rigby has 14,530 mtwo of land

259, 1520, 1521, 1522,260, 1523, 2344, 2345, 3940, 3941