Heron's Formula

If the sides of a triangle measure 3,2 and 1 respectively, what should be the area of the triangle?

#Geometry #VeryInteresting

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

A triangle with these dimensions is not possible. As the sum of two sides of a triangle must be greater than the third side, which is not true in this case. So, the area is zero.

A Former Brilliant Member - 6 years, 5 months ago

Depends on your definition of a triangle. If a triangle is just a set of three points, then the area can be zero; if you prescribe the triangle to have non-collinear points, then the statement is empty.

A Former Brilliant Member - 2 years, 10 months ago

i can prove that the area of triangle is 0 using the heron's formula as you given . as s = 3 when we subract 3 from 3 we get 0. where s is a + b + c/2

sudoku subbu - 6 years, 5 months ago

A triangle with these dimensions is not possible.Since the area of the given triangle is 0

Vishal S - 6 years, 5 months ago

i am also trying to tell that one only dont put seen

sudoku subbu - 6 years, 5 months ago

A Former Brilliant Member - 2 years, 10 months ago

The area is obviously zero.

Sai Ram - 5 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$