Question

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

10, 17, 21

Answer 1

Given: Sides of the triangle are a = 10 cm, b = 17 cm and c = 21 cm.

Step wise calculation:

1. First, calculate the semi-perimeter (s) of the triangle using the formula:

`s = (a + b + c)/2`

= `(10 + 17 + 21)/2`

= `48/2`

= 24

2. Use Heron’s formula for the area (A) of the triangle:

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

= `sqrt(24(24 - 10)(24 - 17)(24 - 21))`

= `sqrt(24 xx 14 xx 7 xx 3)`

3. Calculate the numerical value inside the square root:

24 × 14 = 336,

7 × 3 = 21

336 × 21 = 7056

Thus, `A = sqrt(7056)`

Approximate the square root: `sqrt(7056) ≈ 84  cm^2`

The area of the triangle with sides 10 cm, 17 cm and 21 cm is approximately 84 cm².