Formula for area of a trapezoid
The formula for the area of a trapezoid can be derived by considering the trapezoid as consisting of a rectangle and two right triangles
The formula for the area of a trapezoid can be derived by considering the trapezoid as consisting of a rectangle and two right triangles.
Let’s assume that the trapezoid has two parallel bases, with lengths b1 and b2, and a height h as shown below:
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The area of the trapezoid can be calculated by adding the areas of the rectangle and the two triangles.
1. Area of the rectangle:
The rectangle has a base length equal to the average length of the two bases of the trapezoid, which can be calculated as (b1 + b2) / 2. The height of the rectangle is the same as the height of the trapezoid, h. The formula for the area of a rectangle is simply length × width. Therefore, the area of the rectangle is:
Area of rectangle = (b1 + b2) / 2 × h
2. Area of the triangles:
The two right triangles have bases equal to b1 and b2, and heights equal to h. Thus, each triangle has an area equal to half the product of its base and height. The formula for the area of a triangle is:
Area of the triangle = (1/2) × base × height
Therefore, the combined area of the two triangles is:
Area of triangles = (1/2) × b1 × h + (1/2) × b2 × h
= (b1 + b2) / 2 × h
Adding the area of the rectangle and the area of the triangles, we get the formula for the area of a trapezoid:
Area of trapezoid = (b1 + b2) / 2 × h
So, the area of a trapezoid can be calculated by taking the average of its two bases and multiplying it by the height.
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