Question

Calculate the area of the triangle with the following sides:

33 cm, 44 cm and 55 cm

Answer 1

Given: The triangle has side lengths 33 cm, 44 cm and 55 cm.

Step-wise calculation:

1. Compute the semiperimeter:

`s = (33 + 44 + 55)/2`

= `132/2`

= 66 cm

2. Compute s – a, s – b, s – c:

s – 33 = 33

s – 44 = 22

s – 55 = 11

3. Use Heron’s formula:

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

= `sqrt(66 xx 33 xx 22 xx 11)` 

Note: 66 × 11 = 726 and 33 × 22 = 726.

So, the product is 726 × 726 = 726².

Therefore, Area = `sqrt(726^2)`

= 726 cm²

4. Since 33² + 44²

= 1089 + 1936 

= 3025

= 55² 

The triangle is right-angled with legs 33 and 44. 

So, Area = `(1/2) xx 33 xx 44`

= 726 cm²

The area of the triangle is 726 cm².