# Smallest possible area of triangle

• MHB
• gazparkin
In summary, the conversation is about a question regarding the smallest possible area of a right angled triangle with given measurements. The problem is not clear due to the small size of the image, but the solution involves using the formula for the area of a triangle and considering the given measurements to be rounded to one decimal place. The smallest possible area can be calculated by taking the base and height to be the lowest possible values within their given range.
gazparkin
Hi,

I'm trying to work out this question, and the answer I'm coming up with isn't right. Can anyone help me understand the calculation used to work this out?

#### Attachments

• area Q.jpg
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I can't read that nor enlarge it. Can't you just type the probelm in?

HallsofIvy said:
I can't read that nor enlarge it. Can't you just type the probelm in?
Yes, sorry it's not larger in the browser. The question is, in this right angled triangle, both measurements (2.7cm and 3.4cm) are given correct to 1 decimal place (d.p). What is the smallest possible area of the triangle?

Thank you :)

Okay. I presume you know that the area of such a right triangle is (1/2) base times height. Since the base is 2.7 cm "given to one decimal place", it could be as low as 2.6 cm. The height is 3.4 cm "given to one decimal place" so it could be as low as 3.3 cm. Now can you calculate the smallest area?

## 1. What is the smallest possible area of a triangle?

The smallest possible area of a triangle is 0, which occurs when the triangle is degenerate (has no area) or when the triangle has two sides of length 0.

## 2. What is the formula for finding the smallest possible area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * b * h, where b is the base length and h is the height. However, this formula only applies to non-degenerate triangles. For degenerate triangles, the area is 0.

## 3. Can the smallest possible area of a triangle be negative?

No, the area of a triangle cannot be negative. It is a measure of space, and space cannot have a negative value.

## 4. How does the smallest possible area of a triangle relate to its sides?

The smallest possible area of a triangle is dependent on the lengths of its sides. For non-degenerate triangles, the area will be positive and will increase as the side lengths increase. For degenerate triangles, the area will be 0.

## 5. Is there a limit to how small the area of a triangle can be?

Technically, there is no limit to how small the area of a triangle can be, as long as it is a non-degenerate triangle. However, in practical terms, the smallest possible area of a triangle would be limited by the precision of the measuring tools used to determine its side lengths and the accuracy of the calculations used to find its area.

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