how to make a triangle thats 25 cm²

The formula for the area of a triangle is : A = ba/2

 

25 cm² = ba/2     Multiply both sides by 2

 

50 cm² = ba

 

Any triangle where base*altitude= 50 cm². I choose base = 2 cm and altitude = 25 cm.

The formula for the area of a triangle is base x height x 0.5.

We can use any size base and then use algebra to find out how high the triangle should be.

Base 6

Height x

$${\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\times\,}}{\mathtt{0.5}} = {\mathtt{25}} \Rightarrow {\mathtt{x}} = {\frac{{\mathtt{25}}}{{\mathtt{3}}}} \Rightarrow {\mathtt{x}} = {\mathtt{8.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

Now we know that a triangle with area 25 and base 6cm is 8.3cm high.

You can replace the height and base number with any real positive number.

Now you have 3 points. The two points and the edges of the base line, and at the top of the height line. Now just join them up to get a triangle.