How do you identify the base & perpendicular of a right angled triangle.

triangles

Solution 1:

Any side of a triangle (right or not) can be its base. It is something you choose, so choose whatever is most convenient for your calculation. Once you've chosen a base, the height of the triangle is the distance from the base to the opposite vertex.

For example, to calculate the area of this triangle

We could take

  • $AC$ as base, which has length $4$. The height is the distance from the line $\overleftrightarrow{AC}$ to $B$, which is $3$ (since $\angle A$ is a right angle). Therefore the area is $\frac 12(4)(3) = 6$.
  • $AB$ as base, which has length $3$. The height is the distance to $C$, which is $4$. So the area is $\frac12(3)(4) = 6$.
  • $BC$ as base, which has length $5$. The height is the distance to $A$, which is $2.4$. So the area is $\frac12(5)(2.4) = 6$.

No matter which side we choose as base, the area calculated is the same.

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