Question

Calculate the area of a triangle with sides 15 cm, 36 cm, and 39 cm.

Answer 1

In question only three sides are given.

When we don't know the altitude of a triangle we use Herons formula to find the area of triangle.

Here, a= 15 cm, b= 36cm, c= 39 cm

Semi perimeter (s) =( a+b+c)/2

S= (15+36+39)/2= 90/2= 45

S= 45 cm

Area of ∆ by Heron's Formula =
√s(s-a)(s-b)(s-c)

= √45(45-15)(45-36)(45-39)

= √ 45 × 30× 9 × 6

= √ (5×9)× (6×5) ×(9×6)

√ 5×5×6×6×9×9= 5 × 6× 9

Area of ∆ by Heron's Formula = 270 cm²

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Hope this will help you....

Answer 2

Solution :-

Given : Three sides of a triangle = 15 cm, 36 cm and 39 cm

Then,

a = 15 cm ; b = 36 cm and c = 39 cm

The area of the triangle in this question can be calculated by Heron's Formula.

Semi Perimeter 's' = (a + b + c)/2

⇒ (15 + 36 + 39)/2

⇒ 90/2

⇒ s = 45 cm

Heron's formula of area of triangle = √s(s - a)(s - b)(s - c)

⇒ √45(45 - 15)(45 - 36)(45 - 39)

⇒ √45*30*9*6

⇒ √72900

Area = 270 sq cm

So, the area of the triangle is 270 sq cm

Answer.