A triangle has sides 9, 10 and 17. What is its area by Heron's formula?

1. Heron's formula needs the semi-perimeter s, which is half the perimeter. 2. The perimeter is 9 plus 10 plus 17, which is 36 units. 3. Half of that gives s equal to 18 units. 4. Now form s minus a, s minus b and s minus c: they are 9, 8 and 1. 5. The product s times those three factors is 18 times 9 times 8 times 1, which is 1296. 6. The area is the square root of 1296, which is 36 square units. 7. Answering 18 square units reports the semi-perimeter rather than the area. 8. Answering 72 square units doubles the area, as if the one half were applied twice over. 9. Answering 45 square units multiplies half the base by a height that was never found. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.2 Non-right Triangles: Law of Cosines_