Question

The triangle whose three sides are 15cm 25 cm and 30 cm find the area of the triangle

Answer 1

Here's your answer:-

Area of triangle =√s(s-a)(s-b)(s-c)

s-Semi perimeter of triangle i.e (a+b+c)÷2

s=(15+25+30)÷2=35

Area=√35(35-15)(35-25)(35-20)=187.082

Answer 2

Triangle :--- is a plane figure with three straight sides and three angles.

→ Area of ∆ = 1/2 * Base * Height = 1/2* ab* sinC = 1/2 * bc *sinA = 1/2 * ca* sinB = √( s(s-a)(s-b)(s-c) ) [ where s = (a+b+c)/2 ]

There are three special names given to triangles that tell how many sides (or angles) are equal:---

1) Equilateral Triangle :-- Have Three equal sides and Three equal angles, always 60°..

2) Isosceles Triangle :-- Have Two equal sides and Two equal angles..

3) Scalene Triangle :-- No equal sides and No equal angles...

Triangles can also have names that tell you what type of angle is inside: ---

1) Acute Triangle = All angles are less than 90°..

2) Right Triangle = Has a right angle (90°)..

3) Obtuse Triangle = Has an angle more than 90°..

→ The three interior angles always add to 180°...

___________________

Solution :-

→ 3 sides are Given as 15cm, 25cm & 30cm.

So,

→ Semi-Perimeter = s = (15 + 25 + 30)/2 = 35.

So,

By Heron's formula :-

→ Area of ∆ = √[35(35-15)(35-25)(35-30)]

→ Area of ∆ = √[35 * 20 * 10 * 5 ]

→ Area of ∆ = √[5*7 * 5*4 * 5 * 2 * 5 ]

→ Area of ∆ = √[(5*5) * 4 * (5*5) * (2*7) ]

→ Area of ∆ = 5 * 2 * 5 √14

→ Area of ∆ = 50√14cm². (Ans).