Question

Find the area of a triangle whose sides are 42 cm, 34 cm and 20 cm.

Answer 1

Given: Sides a = 42 cm, b = 34 cm, c = 20 cm.

Step-wise calculation:

1. Semi-perimeter:

`s = (42 + 34 + 20)/2` 

= `96/2`

= 48 cm

2. Heron’s formula: 

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

= `sqrt(48(48 - 42)(48 - 34)(48 - 20))` 

= `sqrt(48 xx 6 xx 14 xx 28)` 

= `sqrt(112896)`

3. Factor/recognize perfect square:

112896 = 336², so `sqrt(112896) = 336`.

Area = 336 cm².