Question

Find the area of triangle ABC if its perimeter is 35cm².

AB: 10cm²
BC: 10cm ²
AC: 15cm ²

Find area by heron's formula.
{ √s(s-a) (s-b) (s-c) }​

Answer 1

Answer:

The area of triangle ABC is 49.69 cm².

Step-by-step-explanation:

We have given that,

For △ABC,

• AB ( a ) = 10 cm
• BC ( b ) = 10 cm
• AC ( c ) = 15 cm
• P ( △ABC ) = 35 cm

We have to find the area of the triangle.

Now,

Semi perimeter ( s ) = Perimeter / 2

⇒ s = P ( △ABC ) / 2

⇒ s = 35 / 2

⇒ s = 17.5 cm

Now, by Heron's formula,

Area of triangle = √[ s ( s - a ) ( s - b ) ( s - c ) ]

⇒ Area of triangle = √[ 17.5 ( 17.5 - 10 ) * ( 17.5 - 10 ) * ( 17.5 - 15 ) ]

⇒ Area of triangle = √[ 17.5 * 7.5 * 7.5 * 2.5 ]

⇒ Area of triangle = 7.5 √( 17.5 * 2.5 )

⇒ Area of triangle = 7.5 √( 2.5 * 7 * 2.5 )

⇒ Area of triangle = 7.5 * 2.5 √7

⇒ Area of triangle = 7.5 * 2.5 * 2.645

⇒ Area of triangle = 7.5 * 2.5 * 2.65

⇒ Area of triangle = 2.5 * 3 * 2.5 * 2.5 * 1.06

⇒ Area of triangle = 6.25 * 3.18 * 2.5

⇒ Area of triangle = 6.25 * 7.95

⇒ Area of triangle = 49.6875

⇒ Area of triangle ≈ 49.69

∴ The area of triangle ABC is 49.69 cm².

Answer 2

Information provided with us:

• Perimeter of a triangle ABC is 35 cm²
• Length of AB = 10 cm²
• Length of BC = 10 cm²
• Length of AC = 15 cm²

What we have to calculate:

• We have to calculate the area of that triangle by using heron's formula

Performing Calculations:

• In order to calculate the area of that triangle we need to first find out the semi perimeter of that triangle.

Formula of semi-perimeter:-

• Semi perimeter = a + b + c / 2

We have,

• a is 10
• b is 10
• c is 15

Substituting the values,

➺ Semi perimeter = 10 + 10 + 15 / 2

➺ Semi perimeter = 20 + 15 / 2

➺ Semi perimeter = 35 / 2

➺ Semi perimeter = 17.5

Finding out the area of triangle by using heron's formula:

• [ √s(s-a) (s-b) (s-c) ]

As we got,

• s is 17.5 cm

Substituting the values of a , b, c and s,

➺ Area = √[17.5 (17.5 - 10) (17.5 - 10) (17.5 - 15)]

➺ Area = √[17.5 (7.5) (7.5) (2.5)

➺ Area = √[17.5 × 7.5 × 7.5 × 2.5]

➺ Area = √[131.25 × 7.5 × 2.5]

➺ Area = √[131.25 × 18.75]

➺ Area = √[2460. 93]

➺ Area = 49.68 (Approx)

• Henceforth, area of triangle by using heron's formula is 49.68cm

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