Triangle Area Formula (Triangle Area Formula)

A triangle is a closed figure formed by connecting three line segments that are not on the same straight line in the same plane. The symbol is △, which is Fundamentals of geometry.

The area of a triangle is the size of a closed figure surrounded by three line segments, and the perimeter of a triangle is the sum of the lengths of the three line segments. The formula for calculating the area of a triangle is: the height of the base is 2, any side of the triangle can be used as the base, the height must be the height of the corresponding base, and the two sides of the right triangle are the base and the height of each other.

A triangle has half the area of a parallelogram with the same base and height. If the areas are equal and the bases are equal, the height of the triangle is twice that of the parallelogram; if the area is equal to the height, the base of the parallelogram is half that of the triangle.

Example 1 What are the common methods for deriving the formula for calculating the area of a triangle? Please show it graphically.

# Graphic thinking

Deduce the formula for calculating the area of a triangle. Use the idea of transformation to transform a triangle into a parallelogram and a rectangle, and use the formulas for calculating the area of a parallelogram and a rectangle to derive the formula for calculating the area of a triangle. Commonly used transformation methods include lattice method, splicing method, cutting and repairing method, folding method and so on. Some methods are as follows:

(1) Stitching method

Using two identical triangles to form a parallelogram.

Because the area of a parallelogram is equal to the base height, the area of a triangle is equal to the base height 2.

(2) Cutting and repairing method

① Cut out a triangle along the center line of the triangle, and move a part of it to the lower right corner of the triangle, so that it can be transformed into a parallelogram . The base of the triangle corresponds to the base of the parallelogram, and the height of the triangle corresponds to half the height of the parallelogram.

Because, the area of the parallelogram = the height of the base, the height of the parallelogram is higher than half of the height of the triangle, and the area of the triangle = the height of the base 2.

②Cut two sides of a triangle from the midpoint along a line parallel to the height, and place the cut part on top to form a rectangle. The long side of the rectangle is equal to the height of the original triangle, and the width is half of the base of the original triangle, so the formula for the area of the triangle is derived.

(3) Use the folding method to deduce, as shown in the figure below: