Question

in∆ABC IF BC=30,AC=24,AB=18 then area of triangle =​

Answer 1

Step-by-step explanation:

Given:-

in∆ABC IF BC=30,AC=24,AB=18

To find:-

Find the area of the ∆ABC?

Solution:-

Method-1:-

Given that

In ∆ABC,

AB= 18 units

BC=30 units

AC =24 units

Let a =30 units ,b=24 units and c=18 units

We know that

If a,b and c are the three sides of a triangle then the area of a triangle is

∆=√[s(s-a)(s-b)(s-c) ] sq.units

Where , s = (a+b+c)/2 units

=>s = (30+24+18)/2 units

=>s=72/2 units

=>s=36 units

On Substituting the values in the above formula then

∆=√[36(36-30)(36-24)(36-18)] sq.units

=>∆=√[36(6)(12)(18)] sq.units

=>∆=√(6×6×6×6×2×2×9) sq.units

=>∆=√[(6×6)×(6×6)×(2×2)×(3×3)] sa.units

=>∆=6×6×2×3 sq.units

=>∆=216 sq.units

Area of the given triangle = 216 sq.units

(or)

Method-2:-

Given sides of ∆ABC are

AB= 18 units

BC=30 units

AC =24 units

AB^2+AC^2

=>(18)^2+(24)^2

=>324+576

=>900

=>(30)^2

= BC^2

AB^2+AC^2 =BC^2

By Pythagoras theorem,

It is clear that it is a right angled triangle and right angle at A

We know that

Area of a right angled triangle is (ab)/2 sq.units

=>(base×height)/2 sq.units

=>(AB×AC)/2 sq.units

=>(18×24)/2 sq.units

=>18×12 sq.units

=>216 sq.units

Area of the given triangle=216 sq.units

Answer:-

Area of the given ∆ABC is 216 sq.units

Used formulae:-

Pythagoras Theorem:-

• In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Heron's Formula:-

• If a,b and c are the three sides of a triangle then the area of a triangle is
• ∆=√[s(s-a)(s-b)(s-c) ] sq.units
• Where , s = (a+b+c)/2 units

Area of a triangle:-

• Area of a triangle = (bh)/2 sq.units, Where "b" is the base and "h" is the height of the triangle.