Question

Find the area of triangle with following sides. [All measures are in cm.]

25, 39, 40

Answer 1

Given: Sides of the triangle are 25 cm, 39 cm and 40 cm.

Step 1: Calculate the semi-perimeter (s) using the formula:

`s = (a + b + c)/2` 

where a = 25, b = 39 and c = 40.

`s = (25 + 39 + 40)/2`

= `104/2`

= 52 cm

Step 2: Calculate the area (A) of the triangle using Heron’s formula: 

`A = sqrt(s(s - a)(s - b)(s - c))`

Calculate each term:

s – a

= 52 – 25

= 27 

s – b

= 52 – 39

= 13

s – c

= 52 – 40

= 12

Step 3: Calculate the area:

`A = sqrt(52 xx 27 xx 13 xx 12)`

Calculate the product inside the square root:

52 × 27 = 1404

1404 × 13 = 18252

18252 × 12 = 219024

Step 4: Calculate the square root:

`A = sqrt(219024) ≈ 468  cm^2`

The area of the triangle with sides 25 cm, 39 cm and 40 cm is approximately 468 cm².