Question

if sides of a triangle are 17 cm 39cm and 42cm find its area​

Answer 1

Given :

✰ Sides of traingle are 17cm, 39cm and 42cm

To Find :

✰ Area of Traingle

Solution :

✰ As in the question sides of traingle are given that is 17cm, 39cm and 42cm. So,Firstly we will find the Semi perimeter or side of traingle that is a + b + c/2, where a, b and c are sides of the Traingle. After Getting the value of semi perimeter. By using the Heron's Formula s(s -a)(s -b)(s-c) where, s is the semi perimeter or side of the Traingle. Hence, we will get the area of traingle.

Let's Solve..!

Semi Perimeter = a + b + c/2

Where,

• a = 17cm

• b = 39cm

• c = 42cm

→ 17 + 39 + 42/2

→ 56 + 42/2

→ 98/2

→ 49cm

Now,Finding Area

Area = s(s - a)(s - b)(s - c)

Where,

• Side (s) = 49cm

→ √49(49 - 17)(49 - 39)(49 - 42)

→ √49 × 32 × 10 × 7

→ √1568 × 10 × 7

→ √15680 × 7

→ √109760

→ 331.30cm²

∴Area of Traingle is 331.30cm²

Answer 2

Given :

• 1st side of Triangle = 17cm
• 2nd side of Triangle = 39cm
• 3rd side of Triangle = 42cm

To Find :

• Area of Triangle

Solution :

✰ As we know that, if three sides of a triangle are given then we have to use Heron's Formula to find the area of the Triangle. Now in this question, Three sides are given so firstly we will find the semi perimeter of the Triangle and then we will apply Heron's Formula to find the area of the Triangle.

⠀

⠀⠀⠀⟼⠀⠀⠀s = a + b + c/2

⠀⠀⠀⟼⠀⠀⠀s = 17 + 39 + 42/2

⠀⠀⠀⟼⠀⠀⠀s = 17 + 81/2

⠀⠀⠀⟼⠀⠀⠀s = 98/2

⠀⠀⠀⟼⠀⠀⠀s = 49cm

⠀

Thus semi perimeter of Triangle is 49cm

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⠀

✰ Now, We will find the area of the Triangle using Heron's Formula.

➟ √s (s - a) (s - b) (s - c)

➟ √49 (49 - 17) (49 - 39) (49 - 42)

➟ √49 × 32 × 10 × 7

➟ √1568 × 70

➟ √109760

➟ 331.30cm²

⠀

Thus Area of Triangle is 331.30cm²

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