# What is the Area of Triangle Abc

What is the Area of Triangle Abc

## Area of Triangles

At that place are several ways to find the area of a triangle.

q8zqH3VR6KY

## Knowing Base and Peak

When we know the base and height it is piece of cake.

It is simply

**half of b times h**

Area =

\frac{one}{2}bh

*(The Triangles page explains more than)*

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

../geometry/images/triangle.js?mode=area

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

(Annotation: 12 is the

**height**, not the length of the left-mitt side)

Height = h = 12

Base = b = twenty

Area =

**½ bh**

= ½ × 20 × 12 =

**120**

627,723, 3132, 3133

## Knowing 3 Sides

In that location’s besides a formula to detect the expanse of whatsoever triangle when we know the lengths of all three of its sides.

This can exist found on the Heron’s Formula page.

## Knowing Two Sides and the Included Angle

When we know two sides and the included angle (SAS), at that place is another formula (in fact 3 equivalent formulas) we can use.

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

Surface area =

\frac{i}{2}ab sin C

Area =

\frac{i}{2}bc sin A

Area =

\frac{1}{two}ca sin B

They are really the same formula, just with the sides and angle changed.

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

First of all we must decide what nosotros know.

Nosotros know bending C = 25º, and sides a = 7 and b = ten.

Then allow’s get going:

**Surface area =**

**(½)ab sin C**

Put in the values we know:

½ × 7 × 10 × sin(25º)

Do some calculator piece of work:

35 × 0.4226…

**Surface area =**

**fourteen.eight**

to ane decimal place

## How to Remember

Only call back “abc”: Surface area = ½

**a**

**b**

sin

**C**

Information technology is besides good to remember that the angle is always

**betwixt the two known sides**, chosen the “included angle”.

## How Does information technology Work?

We start with this formula:

Expanse = ½

**×**

base of operations

**×**

summit

Nosotros know the base is

**c**, and tin work out the height:

the tiptop is

**b × sin A**

So nosotros get:

Surface area = ½ × (c) × (b × sin A)

Which tin can exist simplified to:

Area =

\frac{1}{2}bc sin A

Past changing the labels on the triangle nosotros can too get:

- Surface area = ½ ab sin C
- Area = ½ ca sin B

One more instance:

### Example: Observe How Much State

Farmer Rigby owns a triangular piece of state.

The length of the fence AB is 150 1000. The length of the argue BC is 231 g.

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

How much land does Farmer Rigby own?

Starting time of all we must decide which lengths and angles we know:

- AB = c = 150 chiliad,
- BC = a = 231 chiliad,
- and bending B = 123º

So nosotros apply:

Area =

\frac{1}{2}ca sin B

Put in the values we know:

½ × 150 × 231 × sin(123º) k^{2}

Practice some estimator piece of work:

17,325 × 0.838… 1000^{2}

Area =

14,530 m^{two}

Farmer Rigby has

**14,530 thousand ^{2}
**

of country

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

### What is the Area of Triangle Abc

Source: https://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html