Area of triangles
A triangle is exactly half of a rectangle or parallelogram! Once you know that, you can find its area easily using a simple formula. It's all about base, height, and dividing by two.
Do this: Read the concept below, then try the quiz or activity.
Concept
The area of a triangle is the amount of space inside it. The formula is closely related to the area of a parallelogram.
The Formula: A = ½ x b x h * A stands for Area. * b stands for the base of the triangle. This is one of its sides. * h stands for the height of the triangle. The height is the perpendicular distance from the base to the opposite vertex (corner). It must form a right angle (90°) with the base.
Why does this work? Imagine any triangle. If you make an exact copy of it, you can rotate the copy and fit it together with the original to form a parallelogram. The area of that parallelogram is base x height. Since the triangle is exactly half of that parallelogram, its area is ½ x base x height.
Finding the Base and Height
* The base can be any side of the triangle.
* The height is a line drawn from the opposite corner that is perpendicular to the base. This means it forms a 90° angle.
* In a right triangle, the two legs are the base and height.
* In other triangles, the height might be inside the triangle or sometimes even outside!Example:
A triangle has a base of 10 cm and a height of 6 cm.
1. Formula: A = ½ x b x h
2. Substitute: A = ½ x 10 x 6
3. Solve:
* You can multiply in any order. It's often easiest to multiply the numbers first: 10 x 6 = 60.
* Then take half: ½ of 60 is 30.
* Or, take half of an even number first: ½ of 10 is 5, then 5 x 6 = 30.
4. Answer: The area is 30 square centimeters (30 cm²).Key Idea: The most important part is identifying the correct base and height. The height must always be perpendicular to the base.
Try it
Practice: Area of triangles.