What is the formula to calculate the area of a triangle?
The correct answer and explanation is :
The formula to calculate the area of a triangle is:
[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
]
Explanation:
A triangle is a three-sided polygon, and its area represents the amount of space it occupies in a two-dimensional plane. The formula for the area of a triangle is derived from the basic concept of a rectangle.
- Understanding the Formula
- The base ((b)) of a triangle is any one of its sides, usually chosen based on convenience.
- The height ((h)) is the perpendicular distance from the base to the opposite vertex.
- The multiplication of base and height gives the area of a rectangle if the triangle were duplicated.
- Since a triangle is half of a rectangle when cut diagonally, we divide by 2.
- Why the Formula Works
Imagine a rectangle where the length is the base and the width is the height. The area of such a rectangle is:
[
\text{Area} = b \times h
]
However, a triangle only occupies half of that space, hence:
[
\text{Area of Triangle} = \frac{1}{2} \times b \times h
] - Different Cases and Applications
- For a right triangle, the height is simply one of the perpendicular sides.
- For an acute or obtuse triangle, the height might need to be extended outside the triangle.
- The formula is widely used in geometry, physics, and engineering to compute areas for land surveys, architectural designs, and mechanical structures.
This simple but effective formula helps in various real-world applications where triangular shapes are involved.